Tbilisi Mathematical Journal

On pointwise approximation properties of certain nonlinear Bernstein operators

H. Erhan Altin

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Abstract

The present study is concerned with the nonlinear Bernstein type operators $NB_{n}f$, acting on bounded functions, where the kernel function of the operators provide some convenient assumptions. Especially, some pointwise convergence results for these type operators are achieved at a generalized Lebesgue point of the function $f$.

Note

The author is extremely grateful to the referees for their helpful remarks and valuable suggestions.

Article information

Source
Tbilisi Math. J., Volume 12, Issue 2 (2019), 47-58.

Dates
Received: 10 August 2018
Accepted: 25 February 2019
First available in Project Euclid: 21 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1561082566

Digital Object Identifier
doi:10.32513/tbilisi/1561082566

Mathematical Reviews number (MathSciNet)
MR3973258

Subjects
Primary: 41A35: Approximation by operators (in particular, by integral operators)
Secondary: 41A25: Rate of convergence, degree of approximation 47G10: Integral operators [See also 45P05]

Keywords
nonlinear Bernstein operators pointwise convergence generalized Lebesgue point

Citation

Altin, H. Erhan. On pointwise approximation properties of certain nonlinear Bernstein operators. Tbilisi Math. J. 12 (2019), no. 2, 47--58. doi:10.32513/tbilisi/1561082566. https://projecteuclid.org/euclid.tbilisi/1561082566


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