On approximation properties of generalized Lupaş type operators based on Polya distribution with Pochhammer $k$-symbol

Year 2022, Volume: 51 Issue: 2, 338 - 361, 01.04.2022

Övgü Gürel Yılmaz , Rabia Aktaş , Fatma Taşdelen Yeşildal , Ali Olgun

https://doi.org/10.15672/hujms.911716

Abstract

The purpose of this paper is to introduce a Kantorovich variant of Lupa\c{s}-Stancu operators based on Polya distribution with Pochhammer $k$-symbol. We obtain rates of convergence for these operators by means of the classical modulus of continuity. Also, we give a Voronovskaja type theorem for the pointwise approximation. Furthermore, we construct a bivariate generalization of these operators and we discuss some convergence properties of them. Finally, we present some figures to compare approximation properties of our new operators with those of other operators which are mentioned in this paper. We observe that the approximation of our operators to the function $f$ is better than that of some other operators in a certain range of values of $k$.

Keywords

Bernstein operators, Stancu operators, Lupas operators, Kantorovich operators, Polya distribution, modulus of continuity, Lipschitz class, Voronovskaja type theorem, Pochhammer k-symbol

Supporting Institution

Scientific Research Projects Coordination Unit of Kırıkkale University

Project Number

Project number 2020/045

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