Statistical approximation by $(p,q)$-analogue of Bernstein-Stancu Operators

TL;DR

This paper investigates the approximation properties and convergence behavior of a new class of $(p,q)$-analogue Bernstein-Stancu operators, providing theoretical results and graphical illustrations.

Contribution

It introduces and analyzes the statistical approximation properties of $(p,q)$-Bernstein-Stancu operators, including convergence rates and a Voronovskaja-type theorem.

Findings

Established monotonicity of the operators

Derived a global approximation theorem using Ditzian-Totik modulus

Developed a quantitative Voronovskaja-type theorem

Abstract

In this paper, some approximation properties of $(p,q)$-analogue of Bernstein-Stancu Operators has been studied. Rate of statistical convergence by means of modulus of continuity and Lipschitz type maximal functions has been investigated. Monotonicity of $(p,q)$-Bernstein-Stancu Operators and a global approximation theorem by means of Ditzian-Totik modulus of smoothness is established. A quantitative Voronovskaja type theorem is developed for these operators. Furthermore, we show comparisons and some illustrative graphics for the convergence of operators to a function