Degree of approximation of continuous functions by some singular integrals
Keywords:
Picard, Poisson-Cauchy and Gauss Weierstrass singular integrals, degree of approximation, higher order modulus of smoothnessAbstract
The main aim of this paper is to obtain error bounds in terms of higher order moduli of smoothness, for approximation by singular integrals of Picard, Poisson-Cauchy and Gauss-Weierstrass type.Downloads
References
Th. Angheluţă, IUne remarques sur l'integrale de Poisson, Bull. Sci. Math. (Paris), XVII (1924), 138-140.
N.K. Bari and S.B. Stechkin, Best approximation and differential properties of two conjugate functions,Trudy Moscov, Mat. Oschch. 5 (1956), 483-522 (in Russian).
R.A. DeVore, The Approximation of Continuous Functions by Positive Linear Operators, Springer, Verlag, Berlin, Heidelberg-New York, 1972, https://doi.org/10.1007/bfb0059493
S.G. Gal, Remark on the degree of approximation of continuous functions by singular integrals, Math. Nachr., 164(1993), 197-199, https://doi.org/10.1002/mana.19931640114
G.G. Lorentz, Approximation of Functions, Second Edition Chelsea, 1985.
Approximation by Incomplete Polynomials, In Padé and Rational Approximation, (E.B.,Saff, R.S. Varga Eds), Academic Press, New York, 1977, pp.289-302, https://doi.org/10.1016/b978-0-12-614150-4.50031-9
Gh. Mocică, Problems of Special Functions, Ed. Didactică şi Pedagogică, Bucharet, 1988 (in Romanian).
R.N. Mohapatra and R.S. Rodriguez, On the rate of convergence of singular integrals for Hölder continuous functions, Math. Nachr.149 (1990), 117-124, https://doi.org/10.1002/mana.19901490108
H.S. Shapiro, On some Fourier and Distribution-theoretic Methods in Approximation Theory, In Approximation Theory III, E.W. Cheney (Ed.), Academic Press. New-York-London-Toronto-Sydney-San Francisco, 1980, pp.87-124.
P.C. Xuan, Approximation by linear combinations of Gauss-Weierstrass operators, J. Math. Res. Exposition, 12, 1 (1992), 137-142 (in Chinese with an English summary).
P.C. Xuan, Lp-approximation by linear combinations of Gauss-Weierstrass operators Zhejiang Dauxe Xuebao Ziran Kexue Ban 26, 2 (1992), 131-138 (in Chinese with an English summary).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.