Approximation Of Function By $\alpha-$Baskakov Durrmeyer Type Operators

TL;DR

This paper introduces a generalized form of $ ho$-dependent $ ext{alpha}$-Baskakov Durrmeyer operators, analyzing their approximation properties, convergence rates, and providing numerical validation.

Contribution

It extends existing $ ext{alpha}$-Baskakov Durrmeyer operators by incorporating a real parameter $ ho$, and studies their approximation behavior in various function spaces.

Findings

Operators converge in Korovkin and weighted Korovkin spaces.

Established order and rate of approximation for the operators.

Numerical examples confirm theoretical results.

Abstract

In the present note, we give the generalization of $\alpha-$Baskakov Durrmeyer operators depending on a real parameter $\rho$ > 0. We present the approximation results in Korovkin and weighted Korovkin spaces. We also prove the order of approximation, rate of approximation for these operators. In the end, we verify our results with the help of numerical examples by using Mathematica.