Degree of approximation of continuous functions by some singular integrals

Authors

  • Sorin G. Gal University of Oradea, Romania

Keywords:

Picard, Poisson-Cauchy and Gauss Weierstrass singular integrals, degree of approximation, higher order modulus of smoothness
Abstract views: 236

Abstract

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.

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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).

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Published

1998-08-01

How to Cite

Gal, S. G. (1998). Degree of approximation of continuous functions by some singular integrals. Rev. Anal. Numér. Théor. Approx., 27(2), 251–261. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1998-vol27-no2-art7

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