Generalization of Parametric Baskakov Operators based on the I-P-E distribution

Abstract

This study explores the approximation properties of a non-negative real parametric generalization of the Baskakov operators using the inverse P\'{o}lya-Eggenberger (I-P-E) distribution. As a result of this study, we are able to obtain some approximation results, including Voronovskaya type asymptotic formula, error estimate in terms of modulus of continuity and in sense of k-functional, and weighted approximation.