Bivariate-Schurer-Stancu operators based on (p;q)-integers

TL;DR

This paper introduces a bivariate extension of Shurer-Stancu operators based on (p;q)-integers, providing approximation properties and convergence rates using advanced mathematical tools.

Contribution

It presents a novel bivariate extension of Shurer-Stancu operators based on (p;q)-integers, with proofs of uniform approximation and convergence rates.

Findings

Established uniform approximation using Bohman Korovkin theorem

Derived rate of convergence via total modulus of smoothness

Analyzed degree of approximation with second order modulus

Abstract

The aim of this article is to introduce a bivariate extension of Shurer-Stancu operators based on (p q)integers. We prove uniform approximation by means of Bohman Korovkin type theorem rate of convergence using total modulus of smoothness and degree of approximation by using second order modulus of smoothness Peetres K functional Lipschitz type class.