Some Approximation Properties of the Generalized Baskakov operators

TL;DR

This paper explores a generalized version of Baskakov operators, establishing their approximation properties, convergence behavior, and preservation features using a $ ho$ function, extending classical results.

Contribution

It introduces a generalized Baskakov operator framework and proves new approximation, asymptotic, and convergence results based on a $ ho$ function.

Findings

Established direct theorems for the generalized operators

Derived asymptotic formulas and $A$-statistical convergence results

Extended classical preservation properties to the generalized setting

Abstract

The present paper deals with a generalization of the Baskakov operators. Some direct theorems, asymptotic formula and $A$-statistical convergence are established. Our results are based on a $\rho$ function. These results include the preservation properties of the classical Baskakov operators.