$\alpha$$\beta$-Statistical Convergence of Modified $q$-Durrmeyer Operators

TL;DR

This paper studies the weighted $eta$-statistical approximation properties of modified $q$-Durrmeyer-Stancu operators, providing corrections and analyzing their convergence behavior in the context of $q$-calculus.

Contribution

It introduces new weighted $eta$-statistical convergence results for modified $q$-Durrmeyer-Stancu operators and corrects previous definitions in the literature.

Findings

Established weighted $eta$-statistical approximation properties.

Provided corrections to existing $q$-Durrmeyer-Stancu operators.

Analyzed convergence behavior of the operators.

Abstract

In this work, we investigate weighted $\alpha$$\beta$-Statistical approximation properties of $q$-Durrmeyer-Stancu operators. Also, give some corrections in limit of $q$-Durrmeyer-Stancu operators defined in \cite{mishra2013short} and discuss their convergence properties.