On King Type Modification of $(p,q)$ Baskakov Operators which preserves $x^2$

TL;DR

This paper introduces a modified version of $(p,q)$-Baskakov operators that exactly reproduce the quadratic function $x^2$, analyzing their approximation properties and comparing them graphically with existing operators.

Contribution

The paper develops a new variant of $(p,q)$-Baskakov operators that preserves $x^2$, enhancing approximation capabilities and providing detailed theoretical and graphical analysis.

Findings

Operators reproduce $x^2$ exactly.

Enhanced approximation properties demonstrated.

Graphical comparison shows improvements over original operators.

Abstract

In the present paper, we construct and investigate a variant of modified $(p,q)$-Baskakov operators, which reproduce the test function $x^2$. The order of approximation of the operators via K-functional and second order, usual modulus of continuity, weighted approximation properties are disscussed. In the end some graphical results, comparison with $(p,q)$-Baskakov operators is explained.