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Volumn 20, Issue 1, 2010, Pages 1-21

Asymptotic formulae for bivariate discrete operators: Applications to generalized sampling series and szász-mirak'jan type operators

Author keywords

Generalized sampling series; Moments; Sz sz mirak'jan type operators; Voronovskaja type formula

Indexed keywords


EID: 77949531674     PISSN: 10649735     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (10)

References (33)
  • 1
    • 0347652665 scopus 로고    scopus 로고
    • On the asymptotic approximation with bivariate operators of Bleimann, Butzer, and Hahn
    • U. Abel, On the asymptotic approximation with bivariate operators of Bleimann, Butzer, and Hahn, J. Approx. Theory 97 (1999), 181-198.
    • (1999) J. Approx. Theory , vol.97 , pp. 181-198
    • Abel, U.1
  • 3
    • 29944447013 scopus 로고    scopus 로고
    • Some generalized bivariate Bernstein operators
    • D. Barboau, Some generalized bivariate Bernstein operators, Math. Notes (Miskolc) 1 (1) (2000), 3-10.
    • (2000) Math. Notes (Miskolc) , vol.1 , Issue.1 , pp. 3-10
    • Barboau, D.1
  • 4
    • 33846306231 scopus 로고    scopus 로고
    • On global approximation properties of discrete operators in Orlicz spaces
    • Article 123 (electronic).
    • C. Bardara and I. Mantellini, On global approximation properties of discrete operators in Orlicz spaces, J. Inequal. Pure Appl. Math. 6 (4), (2005), Article 123 (electronic).
    • (2005) J. Inequal. Pure Appl. Math. , vol.6 , pp. 4
    • Bardara, C.1    Mantellini, I.2
  • 5
    • 85064786194 scopus 로고    scopus 로고
    • Approximation properties in abstract modular spaces for a class of general sampling-type operators
    • C. Bardara and I. Mantellini, Approximation properties in abstract modular spaces for a class of general sampling-type operators, Appl. Anal. 85 (2006), 383-413.
    • (2006) Appl. Anal. , vol.85 , pp. 383-413
    • Bardara, C.1    Mantellini, I.2
  • 6
    • 72549095550 scopus 로고    scopus 로고
    • A Voronovskaya-type theorem for a general class of discrete operators
    • C. Bardara and I. Mantellini, A Voronovskaya-type theorem for a general class of discrete operators, Rocky Mountain Math. J. 39 (5) (2009), 1411-1442.
    • (2009) Rocky Mountain Math. J. , vol.39 , Issue.5 , pp. 1411-1442
    • Bardara, C.1    Mantellini, I.2
  • 8
    • 0001606268 scopus 로고
    • Approximation by smooth multivariate splines, Trans
    • C. de Boor and R. DeVore, Approximation by smooth multivariate splines, Trans.. Amer. Math. Soc. 276 (1983), 775-788.
    • (1983) Amer. Math. Soc. , vol.276 , pp. 775-788
    • De Boor, C.1    Devore, R.2
  • 9
    • 51249180153 scopus 로고
    • B-splines from parallelepipeds
    • C. de Boor and K. Höllig, B-splines from parallelepipeds, J. Analyse Math. 42 (1982/1983), 99-115.
    • (1982) J. Analyse Math. , vol.42 , pp. 99-115
    • De Boor, C.1    Höllig, K.2
  • 10
    • 0010923391 scopus 로고
    • Generalized sampling approximation of multivariate signals; theory and some applications
    • P. L. Butzer, A. Fischer, and R. L. Stens, Generalized sampling approximation of multivariate signals; theory and some applications, Note di Matematica 10, Suppl. no.1 (1990), 173-191.
    • (1990) Note di Matematica , vol.10 , Issue.SUPPL. NO.1 , pp. 173-191
    • Butzer, P.L.1    Fischer, A.2    Stens, R.L.3
  • 11
    • 27844471214 scopus 로고
    • Generalized sampling approximation of multivariate signals; general theory
    • P. L. Butzer, A. Fischer, and R. L. Stens, Generalized sampling approximation of multivariate signals; general theory, Atti Sem. Mat. Fis. Univ. Modena 41 (1993), 17-37.
    • (1993) Atti Sem. Mat. Fis. Univ. Modena , vol.41 , pp. 17-37
    • Butzer, P.L.1    Fischer, A.2    Stens, R.L.3
  • 13
    • 0026838009 scopus 로고
    • Sampling theory for not necessarily band-limited functions: An historical overview
    • P. L. Butzer and R. L. Stens, Sampling theory for not necessarily band-limited functions: an historical overview, SIAM Review 34 (1992), 40-53.
    • (1992) SIAM Review , vol.34 , pp. 40-53
    • Butzer, P.L.1    Stens, R.L.2
  • 14
    • 27844557036 scopus 로고
    • Linear prediction by samples from the past. Advanced Topics in Shannon Sampling and Interpolation Theory
    • R.J. Marks II (Ed.) Springer, New York
    • P. L. Butzer and R. L. Stens, Linear prediction by samples from the past. In Advanced Topics in Shannon Sampling and Interpolation Theory, R.J. Marks II (Ed.) Springer Texts Electrical Eng., 157-183, Springer, New York 1993.
    • (1993) Springer Texts Electrical Eng. , pp. 157-183
    • Butzer, P.L.1    Stens, R.L.2
  • 15
    • 0347477832 scopus 로고
    • Multivariate splines. CBMS-NSF regional series in applied mathematics
    • Philadelphia
    • C. K. Chui, Multivariate Splines. CBMS-NSF Regional Series in Applied Mathematics, 54, Soc. Indust. Appl. Math., Philadelphia, 1988.
    • (1988) Soc. Indust. Appl. Math. , vol.54
    • Chui, C.K.1
  • 16
    • 0042254372 scopus 로고
    • s Nonlinear and Convex Analysis (Santa Barbara, Calif. 1985)
    • Dekker, New York
    • s In Nonlinear and Convex Analysis (Santa Barbara, Calif. 1985). Lecture Notes in Pure and Appl. Math., Dekker, New York, (1987), 23-35.
    • (1987) Lecture Notes in Pure and Appl. Math. , pp. 23-35
    • Chui, C.K.1    Lai, H.-C.2
  • 17
    • 77949527326 scopus 로고    scopus 로고
    • A Voronovskaya theorem for a positive linear operator
    • A. Ciupa, A Voronovskaya theorem for a positive linear operator, Soochow J. Math. 31 (3) (2005), 375-387.
    • (2005) Soochow J. Math. , vol.31 , Issue.3 , pp. 375-387
    • Ciupa, A.1
  • 19
    • 23944447076 scopus 로고    scopus 로고
    • On Fejer Bochner-Riesz means
    • Z. Ditzian, On Fejer and Bochner-Riesz means, J. Fourier Anal. Appl. 11 (4) (2005), 489-496.
    • (2005) J. Fourier Anal. Appl. , vol.11 , Issue.4 , pp. 489-496
    • Ditzian, Z.1
  • 20
    • 0010864979 scopus 로고
    • Generalized sampling approximation of multivariate signals; inverse approximation theorems
    • Approximation Theory, Kecskemet, Hungary
    • A. Fischer and R. L. Stens, Generalized sampling approximation of multivariate signals; inverse approximation theorems, Colloquia Mathematica Societatis Janos Bolyai 58 (Approximation Theory, Kecskemet, Hungary), (1990), 275-286.
    • (1990) Colloquia Mathematica Societatis Janos Bolyai 58 , pp. 275-286
    • Fischer, A.1    Stens, R.L.2
  • 21
    • 0003379363 scopus 로고
    • Box splines. Approximation Theory v Proc
    • Edited by C. K. Chui et al., Academic Press, Boston, 1986
    • K. Höllig, Box splines. In: Approximation Theory V Proc Conf. Texas A is M Univ., 1986; Edited by C. K. Chui et al., Academic Press, Boston, 1986, 71-95.
    • (1986) Conf. Texas A Is M Univ. , pp. 71-95
    • Höllig, K.1
  • 22
    • 0003707239 scopus 로고
    • University of Toronto Press, Toronto, 1953, 2 ed., Chelsea Publishing Co., New York
    • G. G. Lorentz, Bernstein polynomials. University of Toronto Press, Toronto, 1953, 2 ed., Chelsea Publishing Co., New York, 1986.
    • (1986) Bernstein Polynomials.
    • Lorentz, G.G.1
  • 23
    • 0038597970 scopus 로고
    • On a numerically efficient method for computing multivariate B-splines. in Multivariate Approximation Theory, Proc
    • Eds. Schempp, W. and Zeller, K., Birkhauser, Basel
    • C. A. Micchelli, On a numerically efficient method for computing multivariate B-splines. In Multivariate Approximation Theory, Proc. Conf. Oberwolfach, (1979), Eds. Schempp, W. and Zeller, K., Birkhauser, Basel, 1979, 211-248.
    • (1979) Conf. Oberwolfach, 1979 , pp. 211-248
    • Micchelli, C.A.1
  • 24
    • 0003311060 scopus 로고
    • Orlicz spaces and modular spaces
    • Springer-Verlag, Berlin
    • J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math., 1034, Springer-Verlag, Berlin, 1983.
    • (1983) Lecture Notes in Math. , pp. 1034
    • Musielak, J.1
  • 25
    • 84931939643 scopus 로고
    • Contributions to the theory of saturation for singular integrals in several variables, III Radial Kernels
    • R. J. Nessel, Contributions to the theory of saturation for singular integrals in several variables, III Radial Kernels, Indagationes Math. 29 (1967), 65-73.
    • (1967) Indagationes Math. , vol.29 , pp. 65-73
    • Nessel, R.J.1
  • 26
    • 77949500494 scopus 로고    scopus 로고
    • About the generalization of Voronovskaja's theorem for Bernstein polynomials of two variables
    • O. T. Pop, About the generalization of Voronovskaja's theorem for Bernstein polynomials of two variables, Int. J. Pure Appl. Math. 38 (3) (2007), 297-308.
    • (2007) Int. J. Pure Appl. Math. , vol.38 , Issue.3 , pp. 297-308
    • Pop, O.T.1
  • 27
    • 77949536205 scopus 로고    scopus 로고
    • The Voronovskaya theorem for some linear positive operators of functions of two variables
    • L. Rempulska and M. Skorupka, The Voronovskaya theorem for some linear positive operators of functions of two variables, Note di Matematica 16 (1) (1996), 145-154.
    • (1996) Note di Matematica , vol.16 , Issue.1 , pp. 145-154
    • Rempulska, L.1    Skorupka, M.2
  • 28
    • 2442546243 scopus 로고    scopus 로고
    • Approximation properties of certain modified Szasz-Mirakyan operators
    • L. Rempulska and Z. Walczak, Approximation properties of certain modified Szasz-Mirakyan operators, Le Matematiche 55 (1) (2000), 121-132.
    • (2000) Le Matematiche , vol.55 , Issue.1 , pp. 121-132
    • Rempulska, L.1    Walczak, Z.2
  • 29
    • 40149106993 scopus 로고    scopus 로고
    • On approximation methods generated by Bochner-Riesz kernels
    • K. V. Runovski and H.-J. Schmeisser, On approximation methods generated by Bochner-Riesz kernels, J. Fourier Anal. Appl. 14 (1) (2008), 16-38.
    • (2008) J. Fourier Anal. Appl. , vol.14 , Issue.1 , pp. 16-38
    • Runovski, K.V.1    Schmeisser, H.-J.2
  • 33
    • 0002663429 scopus 로고
    • Détermination de la forme asymptotique de l'approximation des fonctions par les polynomes de S. Bernstein
    • E. V. Voronovskaja, Détermination de la forme asymptotique de l'approximation des fonctions par les polynomes de S. Bernstein, Dokl. Akad. Nauk SSSR, A (1932), 79-85.
    • (1932) Dokl. Akad. Nauk SSSR, A , pp. 79-85
    • Voronovskaja, E.V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.