Approximation by Modified Jain-Baskakov Operators

TL;DR

This paper investigates the approximation capabilities of modified Jain-Baskakov operators with a parameter c, providing theoretical results including asymptotic formulas and error estimates based on the modulus of continuity.

Contribution

It introduces modified Baskakov basis functions within Jain-Baskakov operators and establishes new approximation results and error bounds.

Findings

Derived asymptotic formulas for the operators.

Established error estimates using modulus of continuity.

Analyzed weighted approximation properties.

Abstract

In the present paper we discuss the approximation properties of Jain-Baskakov operators with parameter c. The present paper deals with the modified forms of the Baskakov basis functions. We establish some direct results, which include the asymptotic formula and error estimation in terms of the modulus of continuity and weighted approximation.