Intelligent Mathematics: Computational Analysis

Intelligent Systems Reference Library

Volumn 5, Issue , 2011, Pages

  Anastassiou, George A ^a  

^a University of Memphis   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84885442325     PISSN: 18684394     EISSN: 18684408     Source Type: Book Series    
DOI: 10.1007/978-3-642-17098-0     Document Type: Article

References (287)

1. Agarwal, R.P.: Difference equations and inequalities. Marcel Dekker, NY (2000)
2. Agarwal, R., Bohner, M.: Basic Calculus on time scales and some of its applications. Results Math. 35(1-2), 3-22 (1999)
3. Agarwal, R., Bohner, M., O'Regan, D.: Time scale systems on infinite intervals. In: Proceedings of the Third World Congress of Nonlinear Analysts, Catania 2000. Part 2 (2000); Nonlinear Anal. 47(2), 837-848 (2001)
4. Agarwal, R., Bohner, M., Peterson, A.: Inequalities on time scales: a survey. Math. Inequalities & Applications 4(4), 535-557 (2001)
5. Agarwal, R.P., Pang, P.Y.H.: Opial Inequalities with Applications in Differential and Difference Equations. Kluwer, Dordrecht (1995)
6. Agrawal, P.N., Kasana, H.S.: On simultaneous approximation by Szász-Mirakian operators. Bull. Inst. Math. Academia Sinica 22, 181-188 (1994)
7. Al-Salam, W.A.: q-Analogues of Cauchy's formulas. Proc. Amer. Math. Soc. 17(3), 616-621 (1966)
8. Ali, S.A., Anastassiou, G.A., Shisha, O.: Discrete Best L-1, Approximation in the Gauges Sense. Numerical Functional Analysis and Optim. 11(5 & 6), 411-417 (1990)
9. Aliprantis, C.D., Burkinshaw, O.: Principles of Real Analysis, 3rd edn. Academic Press, San Diego (1998)
10. Álvarez-Nodarse, R., Atakishiyeva, M.K., Atakishiyev, N.M.: On q-extension of the Hermit Polynomials Hn (x) with the continuous orthogonality property on R. Bol. Soc. Mat. Mexicana 8(3), 127-139 (2002)
11. Anastassiou, G.A.: A study of positive linear operators by the method of moments, Ph.D. Thesis, University of Rochester, N.Y., USA (1984)
12. Anastassiou, G.A.: Rate of convergence of non-positive linear convolution type operators. A sharp inequality. J. Math. Anal. and Appl. 142, 441-451 (1989)
13. Anastassiou, G.A.: Sharp inequalities for convolution type operators. Journal of Approximation Theory 58, 259-266 (1989)
14. Anastassiou, G.A.: Bivariate monotone approximation. Proc. Amer. Math. Soc. 112, 959-964 (1991)
15. Anastassiou, G.A.: Korovkin inequalities for stochastic processes. J. Math. Anal. & Appl. 157(2), 366-384 (1991)
16. Anastassiou, G.A.: Moments in Probability and Approximation Theory. Pitman Research Notes in Math., vol. 287. Longman Sci. & Tech., Harlow (1993)
17. Anastassiou, G.A.: Global smoothness preservation by singular integrals. Proyecciones 14(2), 83-88 (1995)
18. Anastassiou, G.A.: Rate of convergence of some neural networks operators in the univariate case. J. Math. Anal. Appl. 212, 237-262 (1997)
19. Anastassiou, G.A.: Weak convergence of Cardaliaguet-Euvrard neural network operators studied asymptotically. Result. Math. 34(3-4), 214-223 (1998)
20. Anastassiou, G.A.: Degree of approximation of order statistics functionals, Dependent case. In: Anastassiou, G.A. (ed.) Handbook of Analytic Computational Methods in Applied Mathematics, pp. 1-30. Chapman & Hall, CRC, New York (2000)
21. Anastassiou, G.A.: Higher Order Multivariate Wavelet type Approximation. In: He, T. (ed.) Proceedings #941 AMS meeting Wavelet Analysis and Multiresolution Methods, pp. 1-25. Marcel Dekker, New York (2000)
22. Anastassiou, G.A.: Rate of convergence of some multivariate neural networks operators to the unit. Comput. Math. Appl. 40(1), 1-19 (2000)
23. Anastassiou, G.A.: Quantitative Approximations. Chapman & Hall/CRC, Boca Raton, New York (2001)
24. Anastassiou, G.A.: Taylor integral remainders and moduli of smoothness. In: Cho, Y., Kim, J., Dragomir, S. (eds.) Inequality Theory and Applications, vol. 1, pp. 1-13. Nova Science Publishers, Inc., Bombay (2001)
25. Anastassiou, G.A.: Rate of convergence of Bounded Linear operators. In: Shumaker, L. (ed.) Proceedings of 10nth Internat. Conference on Approx. Th., St.Louis, MO, pp. 1-7 (March 2001, 2002)
26. Anastassiou, G.A.: Rate of convergence of Fuzzy Neutral Network operators, univariate case. Journal of Fuzzy Mathematics 10(3), 755-780 (2002)
27. Anastassiou, G.A.: Fuzzy Ostrowski type inequalities. Computational and Applied Mathematics 22(2), 279-292 (2003)
28. Anastassiou, G.A.: High order Approximation by univariate shift-invariant integral operators. In: Agarwal, R., O'Regan, D. (eds.) Nonlinear Analysis and Applications, 2 volumes, 1, pp. 141-164. Kluwer, Dordrecht (2003)
29. Anastassiou, G.A.: Fuzzy Approximation by Fuzzy Convolution type Operators. Computers and Mathematics 48, 1369-1386 (2004)
30. Anastassiou, G.A.: High order Approximation by multivariate shiftinvariant convolution type operators. In: Anastassiou, G.A. (ed.) Computers and Mathematics with Applications, Special issue on Computational Methods in Analysis, vol. 48, pp. 1245-1261 (2004)
31. Anastassiou, G.A.: Higher order Fuzzy Approximation by Fuzzy Wavelet type and Neural Network Operators. Computers and Mathematics 48, 1387-1401 (2004)
32. Anastassiou, G.A.: Univariate fuzzy-random neural network approximation operators. Computers and Mathematics with Applications 48, 1263-1283 (2004)
33. Anastassiou, G.A.: Global Smoothness and Uniform Convergence of Smooth Picard Singular Operators. Computers and Mathematics with Applications 50, 1755-1766 (2005)
34. Anastassiou, G.A.: Basic convergence with rates of smooth Picard singular integral operators. J. Computational Analysis and Appl. 8(4), 313-334 (2006)
35. Anastassiou, G.A.: Higher order Fuzzy Korovkin Theory via Inequalities. Communications in Applied Analysis 10(2), 359-392 (2006)
36. Anastassiou, G.A.: Lp convergence with rates of smooth Picard singular operators. In: Agarwal, R., et al. (eds.) Proceedings of the Inter. Conf. Diff. & Difference Eq. with Appl., held in Melbourne, FLA, Hindawi, NY-Cairo, August 1-5, 2005, pp. 31-45 (2006)
37. Anastassiou, G.A.: Fuzzy Korovkin Theorems and Inequalities. Journal of Fuzzy Mathematics 15(1), 169-205 (2007)
38. Anastassiou, G.A.: Stochastic Korovkin Theory given quantitatively. The Scientific Journal FACTA UNIVERSITATIS, Series Mathematics and Informatics 22(1), 43-60 (2007)
39. Anastassiou, G.A.: Generalized Shisha-Mond type inequality. Anals of Univ. in Oradea, Fascicola Mathematica, Tom XV, 141-143 (2008)
40. Anastassiou, G.A.: Multivariate Stochastic Korovkin Theory given quantitatively. Mathematics and Computer Modeling 48, 558-580 (2008)
41. Anastassiou, G.A.: Balanced Fractional Opial Inequalities. Chaos, Solitons & Fractals 42, 1523-1528 (2009)
42. Anastassiou, G.A.: Fractional Differentiation Inequalities. Springer, Heidelberg (2009)
43. Anastassiou, G.A.: Fractional Korovkin Theory. Chaos, Solitons and Fractals 42, 2080-2094 (2009)
44. Anastassiou, G.A.: On right fractional calculus. Chaos, Solitons and Fractals 42, 365-376 (2009)
45. Anastassiou, G.A.: Basic Inequalities. Revisited, Mathematica Balkanica, New Series 24(Fasc. 1-2), 59-84 (2010)
46. Anastassiou, G.A.: Fractional Trigonometric Korovkin Theory. Communications in Applied Analysis (2009) (accepted)
47. Anastassiou, G.A.: q-inequalities. In: Nonlinear Functional Analysis and Applications, S.Korea (2009) (accepted)
48. Anastassiou, G.A.: Discrete fractional Calculus and inequalities. Mathematica Balkanica (accepted, 2010)
49. Anastassiou, G.A.: Higher order multivariate fuzzy approximation by multivariate fuzzy wavelet type and neural network operators. J. of Fuzzy Mathematics (accepted, 2010)
50. Anastassiou, G.A.: q-fractional inequalities, Cubo (accepted, 2010)
51. Anastassiou, G.A.: Nabla Discrete fractional Calculus and Nabla inequalities. Mathematics and Computer Modelling 51, 562-571 (2010)
52. Anastassiou, G.A.: Duality Principle of Time Scales and Inequalities. Applicable Analysis (accepted, 2010)
53. Anastassiou, G.A.: Foundations of Nabla Fractional Calculus on Time Scales and Inequalities. Computers and Mathematics with Applications 59, 3750-3762 (2010)
54. Anastassiou, G.A.: Fuzzy fractional calculus and Ostrowski inequality. J. of Fuzzy Mathematics (accepted, 2010)
55. Anastassiou, G.A.: Fuzzy global smoothness and fuzzy uniform convergence of fuzzy singular integral operators. J. Fuzzy Mathematics (accepted, 2010)
56. Anastassiou, G.A.: Principles of Delta Fractional Calculus on Time Scales and Inequalities. Mathematics and Computer Modeling 52, 556-566 (2010)
57. Anastassiou, G.A.: Time scales inequalities. Intern. J. of difference equations 5(1), 1-23 (2010)
58. Anastassiou, G.A.: Transfers of real Approximations to vectorial and fuzzy setting. Indian Journal of Mathematics (accepted, 2010)
59. Anastassiou, G.A.: Nabla Time Scales Inequalities, Editor Al. Peterson, special issue on"Time Scales". International Journal of Dynamical Systems and Difference Equations (accepted, 2010)
60. Anastassiou, G.A.: Quantitative Approximation by Fractional Smooth Picard Singular Operators. Mathematics in Engineering Science and Aerospace (accepted, 2010)
61. Anastassiou, G.A., Aral, A.: Generalized Picard Singular Integral. Compt. Math. Appl. 57, 821-830 (2009)
62. Anastassiou, G.A., Aral, A.: On Gauss-Weierstrass type integral operators. Demonstratio Mathematica (accepted, 2010)
63. Anastassiou, G.A., Bendikov, A.: A Sharp Error Estimate for the Numerical Solution of Multivariate Dirichlet Problem. J. Computational and Applied Math. 75, 215-229 (1996)
64. Anastassiou, G.A., Bendikov, A.: A sharp error estimate for the numerical solution of multivariate Dirichlet problem for the heat equation. Stochastic Analysis and Applications 19(3), 343-360 (2001)
65. Anastassiou, G.A., Coroianu, L., Gal, S.G.: Approximation by a nonlinear Cardaliaguet-Euvrard neural network operator of max-product kind. J. Computational Analysis and Applications 12(2), 396-406 (2010)
66. Anastassiou, G.A., Gal, S.G.: On some shift-invariant integral operators, univariate case, revisited. J. Comput. Anal. Appl. 1(1), 3-23 (1999)
67. Anastassiou, G.A., Gal, S.G.: Approximation Theory. Birkhauser, Basel (2000)
68. Anastassiou, G.A., Gal, S.G.: Convergence of generalized singular integrals to the unit, multivariate case. Applied Math. Rev. 1, 1-8 (2000)
69. Anastassiou, G.A., Gal, S.G.: Convergence of generalized singular integrals to the unit, univariate case. Math. Inequalities & Applications 3(4), 511-518 (2000)
70. Anastassiou, G.A., Gal, S.G.: Nonpositive Jackson-type approximations to definite integrals. In: Kopotun, K., Lyche, T., Neamtu, M. (eds.) Trends in Approximation Theory, pp. 11-17. Vanderbilt Press, Nashville (2001)
71. Anastassiou, G.A., Gal, S.G.: On a fuzzy trigonometric approximation theorem of Weierstrass-type. Journal of Fuzzy Mathematics 9(3), 701-708 (2001)
72. Anastassiou, G.A., Gal, S.G.: On some shift-invariant multivariate integral operators, revisited. Communications in Applied Analysis 5(2), 265-275 (2001)
73. Anastassiou, G.A., Gal, S.: Approximation of vector-valued functions by polynomials with coefficients in normed spaces and applications. Demonstratio Mathematica 39(3), 539-552 (2006)
74. Anastassiou, G.A., Gal, S., Ganzburg, M.: A note on shape preserving weighted uniform approximation. Journal of Computational Analysis and Applications 12(1-B), 263-267 (2010)
75. Anastassiou, G.A., Ganzburg, M.I.: L-positive approximation. Romanian J. Pure and Applied Math. XLIII(5/6), 475-494 (1998)
76. Anastassiou, G.A., Ruiz Goldstein, G., Goldstein, J.: Uniqueness for evolution in multidimentional time. Nonlinear Analysis 64, 33-41 (2006)
77. Anastassiou, G.A., Goldstein, J.A.: Fractional Opial type inequalities and fractional differential equations. Math. Results 4, 197-212 (2002)
78. Anastassiou, G.A., Gonska, H.H.: On some shift-invariant integral operators, multivariate case. In: Anastassiou, G.A., Rachev, S.T. (eds.) Proc. Int. Conf. Approx. Prob. and Related Fields, UCSB, Santa Barbara, CA, May 20-22, 1993, pp. 41-64. Plenum Press, New York (1994)
79. Anastassiou, G.A., Gonska, H.H.: On some shift invariant integral operators, univariate case. Ann. Polon. Math. LXI(3), 225-243 (1995)
80. Anastassiou, G.A., Hooshmandasl, M., Ghasemi, A., Moftakharzadeh, F.: Montgomery Identities for Fractional Integrals and Related Fractional Inequalities. Journal of Inequalities in Pure and Applied Mathematics (2009) (accepted)
81. Anastassiou, G.A., Mezei, R.A.: Global Smoothness and Uniform Convergence of Smooth Gauss-Weierstrass Singular Operators. Mathematical and Computer Modelling 50, 984-998 (2009)
82. Anastassiou, G.A., Mezei, R.A.: Global Smoothness and Uniform Convergence of Smooth Poisson-Cauchy Type Singular Operators. Applied Mathematics and Computation 215, 1718-1731 (2009)
83. Anastassiou, G.A., Shisha, O.: Monotone approximation with linear differential operators. J. Approx. Theory 44, 391-393 (1985)
84. Anastassiou, G.A., Yu, X.M.: Bivariate Probabilistic Wavelet Approximation. In: Proceedings of 6th S.E.'Approximation Theory' International Conference, held in Memphis, 1991, pp. 79-92. Marcel Dekker, Inc., New York (1992)
85. Anastassiou, G.A., Yu, X.M.: Convex and Coconvex Probabilistic Wavelet Approximation. Stochastic Analysis and Appl. 10(5), 507-521 (1992)
86. Anastassiou, G.A., Yu, X.M.: Monotone and probabilistic wavelet approximation. Stochastic Analysis and Appl. 10(3), 251-264 (1992)
87. Anastassiou, G.A., Yu, X.M.: Multivariate Probabilistic Approximation in Wavelet Structure. Approx. Th. & Appl. 8(4), 17-27 (1992)
88. Anastassiou, G.A., Yu, X.M.: Probabilistic Discrete Wavelet Approximation. Numer. Func. Anal. Optim. 13(1-2), 117-121 (1992)
89. Anastassiou, G.A., Yu, X.M.: Bivariate Constrained Wavelet Approximation. J. Comp. and Appl. Math. 53, 1-9 (1994)
90. Anastassiou, G.A., Yu, X.M.: Multivariable Probabilistic Scale Approximation. Journal of Fundamental Sciences and Applications, Plovdiv, Bulgaria 5, 41-57 (1997)
91. Anastassiou, G.A., Zhou, M.: On Simultaneous Approximation of Feller Operator. Computers and Mathematics with Appl. 31(10), 31-44 (1996)
92. Anastassiou, G.A., Zhou, M.: Representation Formulae for (Co) mParameter Operator Semigroups. Annales Polonici Mathematici 63(3), 247-272 (1996)
93. Anderson, D.R.: Taylor Polynomials for nabla Dynamic equations on time scales. Panamer. Math. J. 12(4), 17-27 (2002)
94. Anderson, D., Bullock, J., Erbe, L., Peterson, A., Tran, H.: Nabla Dynamic equations on time scales. Panamer. Math. J. 13(1), 1-47 (2003)
95. Aral, A.: On convergence of singular integrals with non-isotropic kernels. Commun. Fac. Sci. Univ. Ank. Series A1 50, 88-98 (2001)
96. Aral, A.: On a generalized λ-Gauss-Weierstrass singular integrals. Fasciculi Mathematici (35), 23-33 (2005)
97. Aral, A.: On the generalized Picard and Gauss Weierstrass Singular Integrals. J. Comp. Anal. and Appl. 8(3), 246-261 (2006)
98. Aral, A.: A generalization of Szász operators based on q-integers. Math. Comput. Modelling 47(9-10), 1052-1062 (2008)
99. Aral, A.: Pointwise approximation by the generalization of Picard and Gauss-Weierstrass singular integrals. Journal of Concrete and Applicable Mathematics 6(4), 327-339 (2008)
100. Aral, A., Doǧru, O.: Bleimann, Butzer and Hahn operators Based on qintegers. Journal of Inequalities and Applications, Article ID 79410, 12 (2007), doi:10.1155/2007/79410
101. Aral, A., Gal, S.G.: q-Generalization of the Picard and Gauss-Weierstrass singular integrals. Taiwanese Journal of Mathematics 12(9), 2501-2515 (2008)
102. Atakishiyev, N.M., Atakishiyeva, M.K.: A q-Analog of the Euler gamma integral. Theo. and Math. Phys. 129(1), 1325-1334 (2001)
103. Atici, F., Biles, D., Lebedinsky, A.: An application of time scales to economics. Mathematical and Computer Modelling 43, 718-726 (2006)
104. Atici, F., Eloe, P.W.: A Transform method in discrete fractional calculus. Intern. J. of Difference Equations 2(2), 165-176 (2007)
105. Atici, F., Eloe, P.W.: Discrete fractional calculus with the nabla operator. Electronic J. of Qualitative Theory of Differential Equations, Spec. Ed. I(1), 1-99 (2009), http://www.math.u-szeged.hu/ejqtde/
106. Atici, F., Eloe, P.W.: Initial value problems in discrete fractional calculus. Proc. AMS 137(3), 981-989 (2009)
107. Barnett, N.S., Dragomir, S.S.: An Ostrowski type inequality for double integrals and applications for cubature formulae. Soochow J. Math. 27(1), 1-10 (2001)
108. Bede, B., Coroianu, L., Gal, S.G.: Approximation and shape preserving properties of the Bernstein operator of max-product kind. Intern. J. Math. Math. Sci., Article ID 590589, 26 (2009), doi:10.1155/2009/590589
109. Bede, B., Gal, S.: Generalizations of the differentiability of fuzzynumbervalued functions with applications to fuzzy differential equations. Fuzzy Sets and Systems 151(3), 581-599 (2005)
110. Bede, B., Gal, S.G.: Approximation by nonlinear Bernstein and FavardSzász-Mirakjan operators of max-product kind. Journal of Concrete and Applicable Mathematics 8(2), 193-207 (2010)
111. Beesack, P.R.: On an integral inequality of Z. Opial. Trans. Amer. Math. Soc. 104, 470-475 (1962)
112. Bernstein, S.N.: Sur les fonctions absolument monotones. Acta Math. 52, 1-66 (1928)
113. Bohner, M., Guseinov, G.S.: Multiple Lebesgue integration on time scales. Advances in Difference Equations, Article ID 26391, 1-12 (2006), doi:10.1155/ADE/2006/26391
114. Bohner, M., Guseinov, G.: Double integral calculus of variations on time scales. Computers and Mathematics with Applications 54, 45-57 (2007)
115. Bohner, M., Guseinov, G.: The Convolution on time scales. Abstract and Applied Analysis, Article ID 58373, 24 (2007)
116. Bohner, M., Luo, H.: Singular second-order multipoint dynamic boundary value problems with mixed derivatives. Advances in Difference Equations, Article ID 54989, 1-15 (2006), doi:10.1155/ADE/2006/54989
117. Bohner, M., Kaymakcalan, B.: Opial inequalities on time scales. Ann. Polon. Math. 77(1), 11-20 (2001)
118. Bohner, M., Matthews, T.: Ostrowski inequalities on time scales. JIPAM. J. Inequal. Pure Appl. Math. 9(1) Article 6, 8 (2008)
119. Bohner, M., Peterson, A.: Dynamic equations on time scales: An Introduction with Applications. Birkhäuser, Boston (2001)
120. Brudnyi, Y.A.: A multidimensional analogue of a theorem of Whitney. Mat. Sbornik 82, 175-191 (1970); English translation: Math. USSR Sb. 11, 157-170 (1970)
121. Butzer, P.L.: On the extension of Bernstein polynomials to the infinite interval. Proc. Amer. Math. Soc. 5, 547-553 (1954)
122. Butzer, P.L., Berens, H.: Semigroups of Operators and Approximation. Springer, New York (1967)
123. Butzer, P.L., Hahn, L.: A probabilistic approach to representation formulae for semigroup of operators with rates of convergence. Semigroup Forum 21, 257-272 (1980)
124. Büttgenbach, B., Esser, H., Lüttgens, G., Nessel, R.J.: A sharp error estimate for the numerical solution of a Dirichlet problem for the Poisson equation. Jour. of Comput. and Appl. Math. 44, 331-337 (1992)
125. Büttgenbach, B., Esser, H., Nessel, R.S.: On the sharpness of error bounds in connection with finite difference schemes on uniform grids for boundary value problems of ordinary differential equations. Numer. Funct. Anal. Optim. 12, 285-298 (1991)
126. Canavati, J.A.: The Riemann-Liouville Integral. Nieuw Archief Voor Wiskunde 5(1), 53-75 (1987)
127. Caputo, M.C.: Time scales: from nabla calculus to delta calculus and vice versa via duality, arxiv: 0910.0085v1 [math.OC] (October 1, 2009)
128. Cardaliaguet, P., Euvrard, G.: Approximation of a function and its derivative with a neural network. Neural Networks 5, 207-220 (1992)
129. Cascaval, R.C., Eckstein, E.C., Frota, C.L., Goldstein, J.A.: Fractional telegraph equations. J. Math. Anal. Appl. 276, 145-159 (2002)
130. Chen, W.Z., Zhou, M.: Freud-Butzer-Hahn type quantitative theorem for probabilistic respresentation of (C0) operator semigroups. Approx. Theory Appl. 9, 1-8 (1993)
131. Cheney, E.W.: Introduction to Approximation Theory. McGraw-Hill, New York (1966)
132. Chernoff, H.: A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Ann. Math. Stat. 23, 493-507 (1952)
133. Chui, C.K., Wang, J.Z.: A Cardinal Spline Approach to Wavelets, CAT Report 211 (1990)
134. Choquet, G.: Lectures on Analysis. Advanced Book Program, vol. I. W.A. Benjamin, Inc. (1969)
135. Chung, K.L.: On the exponential formulas of semi-groups theory. Math. Scand. 19, 153-162 (1962)
136. Congxin, W., Zengtai, G.: On Henstock integral of fuzzy-number-valued functions, I. Fuzzy Sets and Systems 120(3), 523-532 (2001)
137. Csiszar, L.: Information-type measures of difference of probability distributions. Studia Scientiarum Mathematicarum Hungarica 2, 299-318 (1967)
138. Daubechies, I.: Orthonormal bases of compactly supported wavelets. Comm. Pure and Appl. Math. 41, 909-996 (1988)
139. De Sole, A., Kac, V.G.: On integral representations of q-gamma and q-beta functions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16(1), 11-29 (2005)
140. Dem'janovič, J.: Approximation by local functions in a space with fractional derivatives (Lithuanian, English summaries), Differencial'nye Uravnenija i Primenen, Trudy Sem. Processy, 35-49, 103 (1975)
141. DeVore, R.A.: Monotone approximation by polynomials. SIAM J. Math. Anal. 8, 906-921 (1977)
142. DeVore, R.A.: Monotone approximation by splines. SIAM J. Math. Anal. 8, 891-905 (1977)
143. DeVore, R.A., Lorentz, G.G.: Constructive Approximation, vol. 303. Springer, Berlin (1993)
144. Dickmeis, W., Nessel, R.J., van Wickeren, E.: Quantitative extensions of the uniform boundedness principle. Jahr. Deutsch. Math. Verein. 89, 105-134 (1987)
145. Diethelm, K.: Fractional Differential Equations, http://www.tu-bs.de/diethelm/lehre/f-dgl02/fde-skript.ps.gz
146. Dieudonné, J.: Foundations of Modern analysis. Academic Press, London (1969)
147. Doob, J.L.: Classical Potential Theory and its Probabilistic Counterpart. Springer, New York (1984)
148. Dragomir, S.S., Cerone, P., Barnett, N.S., Roumeliotis, J.: An inequlity of the Ostrowski type for double integrals and applications for cubature formulae. Tamsui Cxf. J. Math. Sci. 16(1), 1-16 (2000)
149. Dubois, D., Prade, H.: Fuzzy numbers: An overview, Analysis of fuzzy information. Math. Logic, vol. 1, pp. 3-39. CRC Press, Boca Raton (1987)
150. Dudley, R.: Real Analysis and Probability, Wadsworth & Brooks/Cole Mathematics Series, Pacific Grove, CA (1989)
151. Dynkin, E.B.: Markov Processes. Springer, Berlin (1965)
152. Dynkin, E.B., Yushkievich, A.A.: Markov Processes: Theorems and Problems. Plenum Press, New York (1969)
153. Dzyadyk, V.K.: On the best trigonometric approximation in the L metric of some functions (Russian) Dokl. Akad. Nauk SSSR 129, 19-22 (1959)
154. Eisenberg, S., Wood, B.: Approximating unbounded functions with linear operators generated by moment sequences. Studia Math. 35, 299-304 (1970)
155. El-Sayed, A.M.A., Gaber, M.: On the finite Caputo and finite Riesz derivatives. Electronic Journal of Theoretical Physics 3(12), 81-95 (2006)
156. Ernst, T.: A new notation for q-calculus and a new q- Taylor formula, Uppsala University Report Report. Math., 1-28 (1999)
157. Esser, H., Goebbels, S.J., Lüttgens, G., Nessel, R.J.: Sharp-error bounds for the Crank-Nicholson and Saulyev difference scheme in connection with an initial boundary value problem for the inhomogeneous heat equation. Special Issue on"Concrete Analysis" (guest editor, G. Anastassiou), J. Computers & Mathematics with Applications 30(3-6), 59-68 (1995)
158. Feller, W.: An Introduction to Probability Theory and Its Applications II. Wiley, New York (1966)
159. Feller, W.: An Introduction to Probability Theory and Its Applications, vol. I. Wiley, New York (1968)
160. Frederico, G.S., Torres, D.F.M.: Fractional Optimal Control in the sense of Caputo and the fractional Noether's theorem. International Mathematical Forum 3(10), 479-493 (2008)
161. Freud, G.: On Markov-Bernstein-type inequalities and their applications. J. Aprox. Theory 19, 23-37 (1977)
162. Gadzhiev, A.D.: Theorems of the type of P. P. Korovkin type theorems. Math. Zametki 20(5), 781-786 (1976)
163. Gal, S.G.: Remark on the degree of approximation of continuous functions by singular integrals. Math. Nachr. 164, 197-199 (1993)
164. Gal, S.G.: Degree of approximation of continuous functions by some singular integrals. Rev. Anal. Numér, Théor. Approx. (Cluj), Tome XXVII(2), 251-261 (1998)
165. Gal, S.G.: Approximation Theory in Fuzzy Setting. In: Anastassiou, G. (ed.) Handbook of Analytic-Computational Methods in Applied Mathematics, ch. 13, pp. 617-666. Chapman and Hall/CRC, Boca Raton, New York (2000)
166. Gal, S.G.: Remarks on the Approximation of Normed spaces valued functions by some linear operators. In: Proceedings of 6th Romanian-German research seminar on"Mathematical Analysis and Approximation Theory", pp. 99-109. Mediamira Science Publisher (2004)
167. Gal, S.G.: Shape Preserving Approximation by Real and Complex Polynomials. Birkhauser Publ., Boston (2008)
168. Ganzburg, M.I.: Multidimensional Jackson theorems. Sibirskii Mat. Zhurnal 22(2), 74-83 (1981); English translation: Siberian Math. J. 22, 223-231 (1981)
169. Ganzburg, M.I., Pichugov, S.A.: Invariance of the elements of best approximation and a theorem of Glaeser. Ukrainskii Mat. Zhurnal 33, 664-667 (1981)
170. Gasper, G., Rahman, M.: Basic Hypergeometric Series, Encyclopedia of Mathematics and its Applications, vol. 35. Cambridge University Press, Cambridge (1990)
171. Gauchman, H.: Integral inequalities in q-Calculus. Computers and Mathematics with Applications 47, 281-300 (2004)
172. Goetschel, R., Voxman Jr., V.: Elementary fuzzy calculus. Fuzzy Sets and Systems 18, 31-43 (1986)
173. Goldstein, J.A.: Semigroups of Linear Operators and Applications, Oxford, New York (1985)
174. Gonska, H.H.: Quantitative Korovkin type theorems on simultaneous approximation. Math. Z. 186, 419-433 (1984)
175. Gonska, H.H., Meier, J.: Quantitative theorems on approximation by Bernstein-Stancu operators. Estratto da Calcolo 21(fasc. IV), 317-335 (1984)
176. Gonska, H., Pitul, P., Rasa, I.: On Peano's form of the Taylor remainder, Voronovskaja's theorem and the commutator of positive linear operators. In: Agratini, O., Blaga, P. (eds.) Proceedings of the International Conference on Numerical Analysis and Approximation theory, Cluj-Napoca, Romania, July 5-8, pp. 55-80. Babes-Bolyai University (2006)
177. Gonska, H.H., Zhou, D.-X.: Local Smoothness of functions and BernsteinDurrmeyer Operators. Computers Math. Applic. 30(3-6), 83-101 (1995)
178. Gonska, H.H., Zhou, X.-L.: The strong Converse Inequality for BernsteinKantorovich Operators. Computers Math. Applic. 30(3-6), 103-128 (1995)
179. Gorenflo, R., Mainardi, F.: Essentials of Fractional Calculus, Maphysto Center (2000), http://www.maphysto.dk/oldpages/events/LevyCAC2000/MainardiNotes/fm2k0a.ps
180. Guseinov, G.: Integration on time scales. J. Math. Anal. Appl. 285, 107-127 (2003)
181. Hahn, L.: A note on stochastic methods in connection with approximation theorems for positive linear operators. Pacific J. Math. 101, 307-319 (1981)
182. Hartman, P.: Ordinary Differential Equations. Wiley, New York (1964)
183. Hayman, W.K., Kennedy, P.B.: Subharmonic Functions, vol. 1. Academic Press, London (1976)
184. Hewitt, E., Stromberg, K.: Real and Abstract Analysis. Springer, Berlin (1965)
185. Higgins, R., Peterson, A.: Cauchy functions and Taylor's formula for Time scales T. In: Aulbach, B., Elaydi, S., Ladas, G. (eds.) Proc. Sixth. Internat. Conf. on Difference equations, New Progress in Difference Equations, Augsburg, Germany, 2001, pp. 299-308. Chapman & Hall/CRC (2004)
186. Hilger, S.: Ein Maßketten-Kalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, PhD. thesis, Universität Würzburg, Germany (1988)
187. Hille, E., Phillips, R.S.: Functional Analysis and Semi-groups. Amer. Math. Soc. Coloq. Publ. 31, Providence, R.I. (1957)
188. Hognas, G.: Characterization of weak convergence of signed measures on [0, 1]. Math. Scand. 41, 175-184 (1977)
189. Hsu, L.C.: Approximation of non-bounded continuous functions by certain sequences of linear positive operators of polynomials. Studia Math. 21, 37-43 (1961)
190. Hu, Y.: Convex approximation by quadratic splines. J. Approx. Theory 74(1), 69-82 (1993)
191. Hu, Y., Leviatan, D., Yu, X.M.: Convex polynomial and spline approximation in C[-1, 1]. Constr. Approx. 10, 31-64 (1994)
192. Besov, O.V., Nikolsky, S.M.: The Integral Representation of Functions and Embedding Theorems, Nauka (1975) (in Russian)
193. Ito, K., McKean, M.P.: Diffusion Processes and Their Sample Path. Springer, Berlin (1974)
194. Jackson, F.H.: On a q-definite integrals. Quarterly J. Pure Appl. Math. 41, 193-203 (1910)
195. Jaskólski, M.: Contributions to fractional calculus and approximation theory on the square. Funct. Approx. Comment. Math. 18, 77-89 (1989)
196. Jing, S.C., Fan, H.Y.: q-Taylor's formula with its q- remainder. Comm. Theoret.-Phys. 23(1), 117-120 (1995)
197. Johnen, H., Scherer, K.: On the equivalence of the K-functional and moduli of continuity and some applications. Lect. Notes Math. 571, 119-140 (1977)
198. Johnson, J.: An elementary characterization of weak convergence of measures. The American Math. Monthly 92(2), 136-137 (1985)
199. Kemperman, J.B.: The general moment problem, a geometric approach. Ann. Math. Stat. 39, 93-122 (1968)
200. Kac, V.G., Cheung, P.: Quantum Calculus, Universitext. Springer, New York (2002)
201. Kaleva, O.: Fuzzy Differential Equations. Fuzzy Sets and Systems 24, 301-317 (1987)
202. Kato, T.: Perturbation Theory for Linear Operators. Springer, New York (1966)
203. Khan, M.K.: On the rate of convergence of Bernstein power series for functions of bounded variation. J. Approx. Theory 57, 90-103 (1989)
204. Khan, R.A.: Some probabilistic methods in the theory of approximation operators. Acta Math. Acad. Sci. Hungar. 35, 193-203 (1980)
205. Kim, Y.K., Ghil, B.M.: Integrals of fuzzy-number-valued functions. Fuzzy Sets and Systems 86, 213-222 (1997)
206. Kisynski, J.: Semi-groups of operators and some of their applications to partial differential equations. In: Control Theory and Topics in Functional Analysis, vol. III, pp. 305-405. Internat. Atomic Energy Agency, Vienna (1976)
207. Knoop, H.-B., Pottinger, P.: Ein Satz vom Korovkin-Type fur Ck Raume. Math. Z. 148, 23-32 (1976)
208. Knoop, H.-B., Pottinger, P.: On simultaneous approximation by certain linear positive operators. Arch. Math. 48, 511-520 (1987)
209. Köhnen, W.: Einige Saturationssätze für n-Parametrige Halbgruppen von Operatoren, anal. Numér. Théor. Approx. 9, 65-73 (1980)
210. Koornwinder, T.H.: q-Special Functions, a Tutorial. In: Gerstenhaber, M., Stasheff, J. (eds.) Deformation Theory and Quantum Groups with Applications to Mathematical Physics, Contemp. Math., vol. 134, Amer. Math. Soc., Providence (1992)
211. Kopotun, K.A.: Pointwise and uniform estimates for convex approximation of functions by algebraic polynomials. Constr. Approx. 10, 153-178 (1994)
212. Korovkin, P.P.: Linear Operators and Approximation Theory, Hindustan Publ. Corp., Delhi (1960)
213. Leviatan, D.: Monotone and comonotone polynomial approximation, revisited. J. Approx. Theory 53, 1-16 (1988)
214. Liu, W., Ngô, Q.A., Chen, W.: Ostrowski type inequalities on time scales for double integrals. Acta Appl. Math. 110, 477-497 (2010)
215. Lorentz, G.G.: Bernstein Polynomials. University of Toronto Press, Toronto (1953)
216. Lorentz, G.G., Zeller, K.: Degree of approximation by monotone polynomials I. J. Approx. Theory 1, 501-504 (1968)
217. Lorentz, G.G., Zeller, K.: Degree of approximation by monotone polynomials II. J. Approx. Theory 2, 265-269 (1969)
218. Ma, Z.: Some problems on a variation of L1 approximation, Progress in Approx. Theory, pp. 667-692. Academic Press, Boston (1991)
219. Maizlish, O.: Shape preserving approximation on the real line with exponential weights. J. Approx. Theory 157(2), 127-133 (2009)
220. Mallat, S.G.: Multiresolution approximations and wavelet orthonormal bases of L2 R. Trans. Amer. Math. Soc. 315, 69-87 (1989)
221. Martini, R.: On the approximation of functions together with their derivatives by certain linear positive operators. Indag. Math. 31, 473-481 (1969)
222. Martins, N., Torres, D.: Calculus of variations on time scales with nabla derivatives. Nonlinear Analysis 71(12), 763-773 (2009)
223. Meinardus, G.: Approximation of Functions: Theory and Numerical Methods. Springer Tracts of Natural Philosophy, vol. 4. Springer, New York (1967)
224. Mhaskar, H.N.: Introduction to the Theory of Weighted Polynomial Approximation. Series in Approximations and Decompositions, vol. 7. World Scientific, Singapore (1996)
225. Miller, K.S.: The Weyl Fractional Calculus. In: Ross, B. (ed.) Fractional Calculus and its Applications. Lecture Notes in Mathematics, vol. 457, pp. 80-89. Springer, Berlin (1975)
226. Miller, K.S., Ross, B.: Fractional difference calculus. In: Proc. Intern. Sympos. on Univalent Functions, Fractional calculus and their Appls, Nihon University, Koriyama, Japan (May 1988); Ellis Horwood, Chichester, West Susses, England, pp. 139-152 (1989)
227. Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations, p. 2. John Wiley & Sons, USA (1993)
228. Mitrinović, D.S., Pečarić, J.E., Fink, A.M.: Classical and new inequalities in analysis. Kluwer Academic, Dordrecht (1993)
229. Mitrinović, D.S., Pečarić, J.E., Fink, A.M.: Inequalities for functions and Their integrals and derivatives. Kluwer Academic Publishers, Dordrecht (1994)
230. Mohapatra, R.N., Rodriguez, R.S.: On the rate of convergence of singular integrals for Hölder continuous functions. Math. Nachr. 149, 117-124 (1990)
231. Muntean, I.: Course of Functional Analysis. Spaces of Linear and Continuous Mappings (in Romanian). Faculty of Mathematics, vol. II. Babes-Bolyai University Press, Cluj-Napoca (1988)
232. Nasibov, F.G.: On the degree of best approximation of functions having a fractional derivative in the Riemann-Liouville sense (Russian-Azerbaijani summary), Izv. Akad. Nauk Azerbǎi{dotless}džan. SSR Ser. Fiz.-Mat. Tehn. Nauk (3), 51-57 (1962)
233. Natanson, I.P.: Constructive Function Theory. Ungar, New York (1964)
234. Newman, D.J.: Efficient co-monotone approximations. J. Approx. Theory 25, 189-192 (1979)
235. Olech, C.: A simple proof of a certain result of Z. Opial, Ann. Polon. Math. 8, 61-63 (1960)
236. Opial, Z.: Sur une inegalite. Ann. Polon. Math. 8, 29-32 (1960)
237. Ostrowski, A.: Über die Absolutabweichung einer differentiebaren Function von ihrem Integralmittelwert. Comentarii Mathematici Helvetuci 10, 226-227 (1938)
238. Paltanea, R.: Approximation Theory using positive linear operators. Birkhauser, Boston (2004)
239. Passow, E., Rayman, L., Roulier, J.A.: Comonotone polynomial approximation. J. Approx. Theory 11, 221-224 (1974)
240. Pečarić, J.E.: On the Čebyšev inequality. Bul. Çti. Tehn. Inst. Politehn. "Traian Vuia" Timisoara 25(39)(1), 5-9 (1980)
241. Pečarić, J., Vukelić, A.: Montgomery identities for function of two variables. J. Math. Anal. Appl. 332, 617-630 (2007)
242. Pfeifer, D.: Probabilistic respresentations of operator semigroupsa unifying approach. Semigroup Forum 30, 17-34 (1984)
243. Pfeifer, D.: Approximation-theoretical aspects of probabilistic representations for operator semigroups. J. Approx. Theory 43, 271-296 (1985)
244. Pfeifer, D.: Probabilistic concepts of approximation theory in connection with operator semigroups. Approx. Theory Appl. 1, 93-118 (1985)
245. Pfeifer, D.: A Probabilistic variant of Chernoff's product formula. Semigroup Form 46, 279-285 (1993)
246. Phillips, G.M.: On generalized Bernstein polynomials. In: Griffiths, D.F., Watson, G.A. (eds.) Numerical Analysis, vol. A. R. Mitchell 75th birthday, pp. 263-269. World Scientific, Singapore (1999)
247. Phillips, G.M.: Interpolation and Approximation by Polynomials. Springer, Heidelberg (2003)
248. Pinkus, A., Shisha, O.: Variations on the Chebyshev and Lq theories of best approximation. J. Approx. Theory 35, 148-168 (1982)
249. Popoviciu, T.: Sur l'approximation des fonctions convexes d'ordre superieur. Mathematica (Cluj) 10, 49-54 (1935)
250. Rafi Segi Rahmat, M., Salmi Md Noorani, M.: Fractional integrals and derivatives on time scales with an application (2009) (manuscript)
251. Rajkovic, P.M., Marinkovic, S.D., Stankovic, M.S.: Fractional integrals and derivatives in q-Calculus. Applicable Analysis and Discrete Mathematics 1, 311-323 (2007)
252. Rathore, R.K.S.: Lipschitz-Nikolskii constants for the Gamma operators of Müller. Math. Z. 141, 193-198 (1975)
253. Riesz, F., Sz-Nagy, B.: Functional Analysis. Ungar, New York (1955)
254. Rohatgi, V.K.: An Introduction to Probability Theory and Mathematical Statistics. Wiley-Interscience, New York (1976)
255. Roulier, J.A.: Monotone approximation of certain classes of functions. J. Approx. Theory 1, 319-324 (1968)
256. Royden, H.L.: Real Analysis, 2nd edn. Macmillan, New York (1968)
257. Royden, H.L.: Real Analysis, 3rd edn. Macmillan, New York (1988)
258. Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives, Theory and Applications. Gordon and Breach, Amsterdam (1993); English translation from the Russian, Integrals and Derivatives of Fractional Order and Some of Their Applications, Nauka i Tekhnika, Minsk (1987)
259. Shaw, S.Y.: Approximation of unbounded functions and applications to representations of semigroups. J. Approx. Theory 28, 238-259 (1980)
260. Shaw, S.Y.: Some exponential formulas for m-parameter semigroups. Bull. Inst. Math. Acad. Sinica 9, 221-228 (1981)
261. Shisha, O.: Monotone approximation. Pacific J. Math. 15, 667-671 (1965)
262. Shisha, O., Mond, B.: The degree of approximation to periodic functions by linear positive Operators. Journal of Approximation Theory 1, 335-339 (1968)
263. Shisha, O., Mond, B.: The degree of convergence of sequences of linear positive operators. Nat. Acad. of Sci. U.S. 60, 1196-1200 (1968)
264. Schumaker, L.: Spline Functions. Basic Theory. J. Wiley & Sons, New York (1981)
265. Shvedov, A.S.: Jackson's theorem in Lp, 0 < p < 1, for algebraic polynomials and orders of comonotone approximations. Mat. Zametki 25, 107-117 (1979); English translation: Math. Notes 25, 57-63 (1979)
266. Shvedov, A.S.: Orders of coapproximation of functions by algebraic polynomials. Mat. Zametki 30, 117-130 (1981); English translation: Math. Notes 30, 63-70 (1981)
267. Shvedov, A.S.: Co-convex approximation of functions of several variables by polynomials. Mat. Sbornik 115, 577-589 (1981); English translation: Math. USSR Sb. 43 (1982)
268. Shvedov, A.S.: Approximation of subharmonic functions by subharmonic polynomials. Mat. Zametki 37, 811-819 (1985); English translation: Math. Notes 37, 443-447 (1985)
269. Spitzer, F.: Principles of Random Walk, Graduate Texts in Math, vol. 34. Springer, Heidelberg (1976)
270. Stancu, D.D.: Approximation of functions by a new class of linear polynomial operators. Rev. Roumaine Math. Pures Appl. 13, 1173-1194 (1968)
271. Stancu, D.: Use of probabilistic methods in the theory of uniform approximation of continuous functions. Rev. Roum. Math. Pures et Appl. 14, 673-691 (1969)
272. Stankovic, M., Rajkovic, P., Marinkovic, S.: On q-fractional derivatives of Riemann-Liouville and Caputo type, arXiv: 0909.0387 v1[math.CA] (September 2, 2009)
273. Stein, E.M.: Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton (1970)
274. Stein, E.M., Weiss, G.: Introduction to Fourier Analysis on Euclidean Spaces. Princeton, New Jersey (1971)
275. Tiberiu, T.: Meyer, König and Zeller operators based on the q-integers. Rev. Anal. Numer. Theor. Approx. 29, 221-229 (2002)
276. Timan, A.F.: Theory of Approximation of Functions of a Real Variable. Pergamon Press, Oxford (1963)
277. Wang, R.H.: The Approximation of Unbounded Functions. Sciences Press, Peking (1983) (in Chinese)
278. Weba, M.: Korovkin systems of stochastic processes. Mathematische Zeitschrift 192, 73-80 (1986)
279. Weba, M.: A quantitative Korovkin theorem for random functions with multivariate domains. J. Approx. Theory 61, 74-87 (1990)
280. Welhelmsen, D.R.: A Markov inequality in several dimensions. J. Approx. Theory 11, 216-220 (1974)
281. Whittaker, E.T., Watson, G.N.: A Course in Modern Analysis. Cambridge University Press, Cambridge (1927)
282. Wu, C., Gong, Z.: On Henstock integral of fuzzynumbervalued functions (I). Fuzzy Sets and Systems 120(3), 523-532 (2001)
283. Wu, C., Ma, M.: On embedding problem of fuzzy number spaces: Part 1. Fuzzy Sets and Systems 44, 33-38 (1991)
284. Xiong, X.: The best asyptotic constant of a class of approximation operators. J. Approx. Theory 70, 348-357 (1992)
285. Yüksel, I., Ispir, N.: Weighted approximation by a certain family of summation integral-type operators. Compt. Math. Appl. 52, 1463-1470 (2006)
286. Zadeh, L.A.: Fuzzy Sets. Inform. and Control 8, 338-353 (1965)
287. Zhang, Y.Q., Cao, F.L., Xu, Z.B.: Approximation by neural network operators of Cardaliaguet-Euvrard type (Chinese; English summary). Acta Math. Sinica (Chinese series) 51(6), 1161-1174 (2008)