Better approximation of functions by genuine Bernstein-Durrmeyer type operators

TL;DR

This paper introduces a new class of Bernstein-Durrmeyer operators with improved approximation features, providing theoretical estimates, asymptotic formulas, and numerical validation to demonstrate enhanced convergence properties.

Contribution

The paper develops a novel genuine Bernstein-Durrmeyer operator with superior approximation capabilities over classical versions.

Findings

The new operators have better approximation features.

Direct estimates are provided using modulus of continuity.

Numerical examples confirm improved convergence rates.

Abstract

The main object of this paper is to construct a new genuine Bernstein-Durrmeyer type operators which have better features than the classical one. Some direct estimates for the modified genuine Bernstein-Durrmeyer operator by means of the first and second modulus of continuity are given. An asymptotic formula for the new operator is proved. Finally, some numerical examples with illustrative graphics have been added to validate the theoretical results and also compare the rate of convergence.