Deferred Nörlund statistical relative uniform convergence and Korovkin-type approximation theorem

Year 2021, Volume: 70 Issue: 1, 279 - 289, 30.06.2021

Kamil Demirci , Fadime Dirik , Sevda Yıldız

https://doi.org/10.31801/cfsuasmas.807169

Cited By: 4

Abstract

In this paper, we define the concept of statistical relative uniform convergence of the deferred Nörlund mean and we prove a general Korovkin-type approximation theorem by using this convergence method. As an application, we use classical Bernstein polynomials for defining an operator that satisfies our new approximation theorem but does not satisfy the theorem given before. Additionally, we estimate the rate of convergence of approximating positive linear operators by means of the modulus of continuity.

Keywords

Statistical convergence, statistical relative uniform convergence, Nörlund summability, Korovkin-type approximation theorem, modulus of continuity

Supporting Institution

Sinop University

Project Number

FEF-1901-18-25.

Thanks

This research was supported by Sinop University Scientific Research Coordination Unit, Project N. FEF-1901-18-25.

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