B\'{e}zier Variant of generalized Bernstein-Durrmeyer type operators

TL;DR

This paper introduces a Bézier variant of generalized Bernstein-Durrmeyer operators, providing error estimates and analyzing approximation rates for functions of bounded variation, expanding the theoretical framework of these operators.

Contribution

It defines a new Bézier variant of the operators and derives error bounds and approximation rates, extending existing operator theory.

Findings

Error estimates in terms of Ditzian-Totik modulus of smoothness

Approximation rates for functions of bounded variation

Extension of operator approximation theory

Abstract

In this paper, we define B\'{e}zier variant of generalized Bernstein-Durrmeyer type operators of second order, introduced by Ana et al. Then, we find an error estimate in terms of terms of Ditzian Totik modulus of smoothness. Next, we study the rate of approximation for a larger class of functions of bounded variation.