On King type modification of $(p,q)$-Lupa\c{s} Bernstein operators

TL;DR

This paper introduces a King-type modification of $(p,q)$-Lupa ext{š} Bernstein operators, analyzes their convergence properties, and demonstrates improved error estimates over certain subintervals compared to the original operators.

Contribution

The paper presents a novel King-type modification of $(p,q)$-Lupa ext{š} Bernstein operators and studies their convergence and error estimation.

Findings

Modified operators show better error estimates on some subintervals.

Convergence analyzed using modulus of continuity and Lipschitz class.

Error bounds are improved over original $(p,q)$-Lupa ext{š} Bernstein operators.

Abstract

In this paper, a King-type modification of $(p,q)$-Lupa\c{s} Bernstein operators are introduced. The rate of convergence of these operators are studied by means of modulus of continuity and Lipschitz class functional. Further, it has been shown that the error estimation of these operators on some subintervals of $[0,1]$ are better than the $(p,q)$-Lupa\c{s} Bernstein operators.