Basic convergence with rates of smooth picard singular integral operators

Journal of Computational Analysis and Applications

Volumn 8, Issue 4, 2006, Pages 313-334

  Anastassiou, George A ^a  

^a University of Memphis   (United States)

Author keywords

Best constant; Modulus of smoothness; Picard singular integral; Sharp inequality

Indexed keywords

EID: 33751066945     PISSN: 15211398     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. G.A. Anastassiou, Rate of convergence of non-positive linear convolution type operators. A sharp inequality, J. Math. Anal.and Appl., 142 (1989), 441-451.
2. G.A. Anastassiou, Sharp inequalities for convolution type operators, Journal of Approximation Theory, 58 (1989), 259-266.
3. G.A. Anastassiou, Moments in Probability and Approximation Theory, Pitman Research Notes in Math., Vol. 287, Longman Sci. & Tech., Harlow, U.K., 1993.
4. G.A. Anastassiou, Quantitative Approximations, Chapman & Hall/CRC, Boca Raton, New York, 2001.
5. G.A. Anastassiou and S. Gal, Convergence of generalized singular integrals to the unit, univariate case, Math. Inequalities & Applications, 3, No. 4 (2000), 511-518.
6. G.A. Anastassiou and S. Gal, Convergence of generalized singular integrals to the unit, multivariate case, Applied Math. Rev., Vol. 1, World Sci. Publ. Co., Singapore, 2000, pp. 1-8.
7. R.A. DeVore and G.G. Lorentz, Constructive Approximation, Springer-Verlag, Vol. 303, Berlin, New York, 1993.
8. S.G. Gal, Remark on the degree of approximation of continuous functions by singular integrals, Math. Nachr., 164 (1993), 197-199.
9. S.G. Gal, Degree of approximation of continuous functions by some singular integrals, Rev. Anal. Numér, Théor. Approx., (Cluj), Tome XXVII, No. 2 (1998), 251-261.
10. J.B. Kemperman, The general moment problem, a geometric approach, Ann. Math. Stat., 39 (1968), 93-122.
11. R.N. Mohapatra and R.S. Rodriguez, On the rate of convergence of singular integrals for Holder continuous functions, Math. Nachr., 149 (1990), 117-124.
12. L. Schumaker, Spline Functions. Basic Theory, J. Wiley & Sons, New York, 1981.