On approximation by Stancu type q-Bernstein-Schurer-Kantorovich operators

TL;DR

This paper introduces a generalized class of q-Bernstein-Schurer-Kantorovich operators, analyzes their approximation properties, convergence behavior, and extends the study to bivariate cases, providing new theoretical insights.

Contribution

It presents a new Stancu type generalization of q-Bernstein-Schurer-Kantorovich operators and explores their approximation and convergence properties, including bivariate extensions.

Findings

Operators converge in the Lipschitz class

Statistical Korovkin's theorem confirms convergence

Direct approximation theorems established

Abstract

In this paper we introduce the Stancu type generalization of the q-Bernstein-Schurer-Kantorovich operators and examine their approximation properties. We investigate the convergence of our operators with the help of the Korovkin's approximation theorem and examine the convergence of these operators in the Lipschitz class of functions. We also investigate the approximation process for these operators through the statistical Korovkin's approximation theorem. Also, we present some direct theorems for these operators. Finally we introduce the bivariate analogue of these operators and study some results for the bivariate case.