Stancu-variant of generalized Baskakov operators

TL;DR

This paper introduces a Stancu-variant of generalized Baskakov operators, analyzing their convergence rate, approximation order, and establishing a Voronovskaya-type theorem to deepen understanding of their mathematical properties.

Contribution

The paper presents a new Stancu-variant of generalized Baskakov operators and investigates their convergence behavior and approximation properties.

Findings

Established the rate of convergence using modulus of continuity

Derived direct estimates with K-functional and Ditzian-Totik modulus

Proved a Voronovskaya-type theorem for the operators

Abstract

In the present paper, we introduce Stancu-variant of generalized Baskakov operators and study the rate of convergence using modulus of continuity, order of approximation for the derivative of function f . Direct estimate is proved using K-functional and Ditzian-Totik modulus of smoothness. In the last, we have proved Voronovskaya type theorem.