On Simultaneous Approximation of Modified Baskakov Durrmeyer Operators

TL;DR

This paper investigates the properties and convergence behavior of modified Baskakov-Durrmeyer-Stancu operators with a parameter, providing moments, asymptotic formulas, and error estimates to understand their approximation capabilities.

Contribution

It introduces and analyzes a new class of modified Baskakov-Durrmeyer-Stancu operators, deriving their moments, convergence properties, and asymptotic behavior.

Findings

Established point-wise convergence of the operators.

Derived Voronovskaja type asymptotic formula.

Provided error estimates based on second order modulus of continuity.

Abstract

In this present manuscript, we discuss properties of modified Baskakov-Durrmeyer-Stancu (BDS) operators with parameter $\gamma>0$. We compute the moments of these modified operators. Also, establish point-wise convergence, Voronovskaja type asymptotic formula and an error estimation in terms of second order modification of continuity of the function for the operators $B_{n,\gamma}^{\alpha,\beta}(f,x)$.