(p,q)-Beta Functions and Applications in Approximation

TL;DR

This paper introduces (p,q)-Beta functions and their application in creating modified Bernstein polynomials, providing approximation estimates and visualizing convergence behavior for various parameters.

Contribution

It develops a new (p,q)-analogue of Beta operators and applies them to modify Bernstein polynomials, offering novel approximation tools.

Findings

Derived direct approximation results for (p,q)-Bernstein operators

Provided graphical illustrations of convergence for different parameters

Demonstrated the effectiveness of (p,q)-approximations in visualization

Abstract

In the present paper, we consider (p,q)-analogue of the Beta operators and using it, we propose the integral modification of the generalized Bernstein polynomials. We estimate some direct results on local and global approximation. Also, we illustrate some graphs for the convergence of (p,q)-Bernstein-Durrmeyer operators for different values of the parameters p and q using Mathematica package.