Research Article

On some approximation properties of the Gauss-Weierstrass operators

Volume: 68 Number: 2 August 1, 2019
EN

On some approximation properties of the Gauss-Weierstrass operators

Abstract

In this paper, we present some approximation properties of the Gauss-Weierstrass operators in exponential weighted spaces including norm convergence of them and Voronovskaya and quantitative Voronovskaya-type theorems.

Keywords

References

  1. Anastassiou, G. A.,Aral, A., On Gauss-Weierstrass type integral oprators. Demonstratio Mathematica 43(2010), no.4, 841--849.
  2. Becker , M., Kucharski, D., Nessel, R. J., Global approximation theorems for the Szasz- Mirakyan operators in exponential weight spaces, in Linear Spaces and Approximation, Proc. Conf. Oberwolfach, 1977), Birkhauser Verlag, Basel (1978), pp. 319-333.
  3. Butzer, P.L., Nessel, R.J. Fourier Analysis and Approximation, I,II; Birkhauser, Basel and Academic Press, New York, 1971
  4. Deeba, E., Mohapatra, R.N., Rodriguez, R. S., On the degree of approximation of some singular integrals, Rend. Mat. Appl. 7(1988), 345-355.
  5. Ditzian, Z., Totik, V., Moduli of Smoothness, Springer-Verlag, New-York, 1987.
  6. Ibragimov, I. I, Theory of Approximation by Entire Functions, in Russian, Baku, 1979.
  7. Leśniewicz, A., Rempulska, L., Wasiak, J., Approximation properties of the Picard singular integral in exponential weight spaces, Publ. Mat. 40(1996), no.2, 233--242.
  8. Mohapatra, R.N., Rodriguez, R.S., On the rate of convergence of singular integrals for Hölders continuous functions.Math. Nachr. 149(1990), 117-124.

Details

Primary Language

English

Subjects

Applied Mathematics

Journal Section

Research Article

Publication Date

August 1, 2019

Submission Date

January 9, 2019

Acceptance Date

May 31, 2019

Published in Issue

Year 2019 Volume: 68 Number: 2

APA
Yılmaz, B. (2019). On some approximation properties of the Gauss-Weierstrass operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 2154-2160. https://doi.org/10.31801/cfsuasmas.510560
AMA
1.Yılmaz B. On some approximation properties of the Gauss-Weierstrass operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):2154-2160. doi:10.31801/cfsuasmas.510560
Chicago
Yılmaz, Başar. 2019. “On Some Approximation Properties of the Gauss-Weierstrass Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 (2): 2154-60. https://doi.org/10.31801/cfsuasmas.510560.
EndNote
Yılmaz B (August 1, 2019) On some approximation properties of the Gauss-Weierstrass operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 2154–2160.
IEEE
[1]B. Yılmaz, “On some approximation properties of the Gauss-Weierstrass operators”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 2154–2160, Aug. 2019, doi: 10.31801/cfsuasmas.510560.
ISNAD
Yılmaz, Başar. “On Some Approximation Properties of the Gauss-Weierstrass Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 1, 2019): 2154-2160. https://doi.org/10.31801/cfsuasmas.510560.
JAMA
1.Yılmaz B. On some approximation properties of the Gauss-Weierstrass operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:2154–2160.
MLA
Yılmaz, Başar. “On Some Approximation Properties of the Gauss-Weierstrass Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, Aug. 2019, pp. 2154-60, doi:10.31801/cfsuasmas.510560.
Vancouver
1.Başar Yılmaz. On some approximation properties of the Gauss-Weierstrass operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019 Aug. 1;68(2):2154-60. doi:10.31801/cfsuasmas.510560

Cited By

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

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