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On some approximation properties of the Gauss-Weierstrass operators

Year 2019, , 2154 - 2160, 01.08.2019
https://doi.org/10.31801/cfsuasmas.510560

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.

References

  • Anastassiou, G. A.,Aral, A., On Gauss-Weierstrass type integral oprators. Demonstratio Mathematica 43(2010), no.4, 841--849.
  • 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.
  • Butzer, P.L., Nessel, R.J. Fourier Analysis and Approximation, I,II; Birkhauser, Basel and Academic Press, New York, 1971
  • Deeba, E., Mohapatra, R.N., Rodriguez, R. S., On the degree of approximation of some singular integrals, Rend. Mat. Appl. 7(1988), 345-355.
  • Ditzian, Z., Totik, V., Moduli of Smoothness, Springer-Verlag, New-York, 1987.
  • Ibragimov, I. I, Theory of Approximation by Entire Functions, in Russian, Baku, 1979.
  • 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.
  • Mohapatra, R.N., Rodriguez, R.S., On the rate of convergence of singular integrals for Hölders continuous functions.Math. Nachr. 149(1990), 117-124.
  • Rempulska, L. and Tomczak, K., On some properties of the Picard operators, Arch. Math. (Brno), 45(2009), 125-135.
Year 2019, , 2154 - 2160, 01.08.2019
https://doi.org/10.31801/cfsuasmas.510560

Abstract

References

  • Anastassiou, G. A.,Aral, A., On Gauss-Weierstrass type integral oprators. Demonstratio Mathematica 43(2010), no.4, 841--849.
  • 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.
  • Butzer, P.L., Nessel, R.J. Fourier Analysis and Approximation, I,II; Birkhauser, Basel and Academic Press, New York, 1971
  • Deeba, E., Mohapatra, R.N., Rodriguez, R. S., On the degree of approximation of some singular integrals, Rend. Mat. Appl. 7(1988), 345-355.
  • Ditzian, Z., Totik, V., Moduli of Smoothness, Springer-Verlag, New-York, 1987.
  • Ibragimov, I. I, Theory of Approximation by Entire Functions, in Russian, Baku, 1979.
  • 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.
  • Mohapatra, R.N., Rodriguez, R.S., On the rate of convergence of singular integrals for Hölders continuous functions.Math. Nachr. 149(1990), 117-124.
  • Rempulska, L. and Tomczak, K., On some properties of the Picard operators, Arch. Math. (Brno), 45(2009), 125-135.
There are 9 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Review Articles
Authors

Başar Yılmaz 0000-0003-3937-992X

Publication Date August 1, 2019
Submission Date January 9, 2019
Acceptance Date May 31, 2019
Published in Issue Year 2019

Cite

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

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

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