On Approximation by $(p,q)$-Meyer-König-Zeller Durrmeyer Operators

Document Type : Original Article

Authors

Honey Sharma ¹

Cheena Gupta ²

Ramapati Maurya ³

¹ Department of Mathematics, Gulzar Group of Institutes, Punjab, India.

² I K G Punjab Technical University, Punjab, India.

³ I K G Punjab Technical University, Punjab, India; Department of Mathematics, Manav Rachna University, Haryana, India.

10.22034/kjm.2019.81223

Abstract

In this paper, we introduce a Durrmeyer type modification of Meyer-König-Zeller operators based on $(p,q)$-integers. The rate of convergence of these operators is explored with the help of Korovkin type theorems. We establish some direct results for proposed operators. We also obtain statistical approximation properties of operators. In the last section, we show the rate of convergence of $(p,q)$-Meyer-König-Zeller Durrmeyer operators for some functions by means of MATLAB programming.

Keywords

$(p, q)$-Calculus, $(p, q)$-Meyer-König-Zeller operator

modulus of continuity

Peetre $K$-functional

statistical convergence

Subjects

• 41 Approximations and expansions

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