Journal of Applied Mathematics and Computation

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Article http://dx.doi.org/10.26855/jamc.2021.12.016

Weighted Approximation Properties of New (p, q)—Analogue of Balazs Szabados Operators

Hayatem Hamal1,2,*, Pembe Sabancıgil1,2

1Department of Mathematics, Faculty of Education Janzour, Tripoli University, Tripoli, Libya.

2Department of Mathematics, Eastern Mediterranean University, Gazimagusa, North Cyprus.

*Corresponding author: Hayatem Hamal

Published: December 30,2021

Abstract

Korovkin-type theorems provide simple and useful tools for finding out whether a given sequence of positive linear operators, acting on some function space is an approximation processor, equivalently, converges strongly to the identity operator. These theorems exhibit a variety of test subsets of functions which guarantee that the approximation property holds on the whole space provided it holds on them. These kinds of results are called “Korovkin-type theorems” which refers to P.P. Korovkin who in 1953 discovered such a property for the functions 1, X and X2   in the space C([0,1]). After this discovery, several mathematicians have undertaken the program of extending Korovkin’s theorems in many ways and to several settings. Such developments delineated a theory which is nowadays referred to as Korovkin-type approximation theory. In this paper, we study weighted approximation properties of new (p, q) - analogue of the Balázs-Szabados operators by using the weighted modulus of continuity and we give a Korovkin type theorem for weighted approximation.

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How to cite this paper

Weighted Approximation Properties of New (p, q)—Analogue of Balazs Szabados Operators

How to cite this paper: Hayatem Hamal, Pembe Sabancıgil. (2021) Weighted Approximation Properties of New (p, q)—Analogue of Balazs Szabados OperatorsJournal of Applied Mathematics and Computation5(4), 373-381.

DOI: http://dx.doi.org/10.26855/jamc.2021.12.016