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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


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Volume 60, Issue 2

Issues

Theorems for generalized Favard-Kantorovich and Favard-Durrmeyer operators in exponential function spaces

Grzegorz Nowak / Aneta Sikorska-Nowak
Published Online: 2010-02-21 | DOI: https://doi.org/10.2478/s12175-010-0011-0

Abstract

We consider the Kantorovich and the Durrmeyer type modifications of the generalized Favard operators and we prove some direct approximation theorems for functions f such that w σ f ∈ L p(R), where 1 ≤ p ≤ ∞ and w σ(x) = exp(−σx 2), σ > 0.

MSC: Primary 41A25

Keywords: Favard-Kantorovich operator; Favard-Durrmeyer operator; direct approximation theorem; exponential weight space; weighted modulus of smoothness

  • [1] BECKER, M.— BUTZER, P. L.— NESSEL, R. J.: Saturation for Favard operators in weighted function spaces, Studia Math. 59 (1976), 139–153. Google Scholar

  • [2] BECKER, M.: Inverse theorems for Favard operators in polynomial weight spaces, Ann. Soc. Math. Polon. Ser. I: Comment. Math. 22 (1981), 165–173. Google Scholar

  • [3] BUTZER, P. L.— NESSEL, R. J.: Fourier Analysis and Approximation, Vol. I, Academic Press, New York-London, 1971. Google Scholar

  • [4] FAVARD, J.: Sur les multiplicateurs d’interpolation, J. Math. Pures Appl. 23 (1944), 219–247. Google Scholar

  • [5] GAWRONSKI, W.— STADTM-ULLER, U.: Approximation of continuous functions by generalized Favard operators, J. Approx. Theory 34 (1982), 384–396. http://dx.doi.org/10.1016/0021-9045(82)90081-8CrossrefGoogle Scholar

  • [6] NOWAK, G.— PYCH-TABERSKA, P.: Approximation properties of the generalized Favard-Kantorovich operators, Ann. Soc. Math. Polon. Ser. I: Comment.Math. 39 (1999), 139–152. Google Scholar

  • [7] NOWAK, G.— PYCH-TABERSKA, P.: Some properties of the generalized Favard-Durrmeyer operators, Funct. Approx. Comment. Math. 29 (2001), 103–112. Google Scholar

  • [8] PYCH-TABERSKA, P.: On the generalized Favard operators, Funct. Approx. Comment. Math. 26 (1988), 265–273. Google Scholar

About the article

Published Online: 2010-02-21

Published in Print: 2010-04-01


Citation Information: Mathematica Slovaca, Volume 60, Issue 2, Pages 265–278, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-010-0011-0.

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© 2010 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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