The equivalent theorem of a new generalized Bernstein-Bezier operators

TL;DR

This paper introduces a new class of generalized Bernstein-Bezier operators, analyzes their moments, convergence rate, and establishes an equivalent theorem to understand their approximation properties.

Contribution

The paper constructs a novel generalized Bernstein-Bezier operator and studies its moments, convergence, and an equivalent theorem, expanding the theoretical framework of approximation operators.

Findings

Operators' moments are estimated.

Convergence rate is established via modulus of continuity.

An equivalent theorem for these operators is proved.

Abstract

In this paper, a new generalized Bernstein-Bezier type operators is constructed.The estimates of the moments of these operators are investigated. The rate of convergence in terms of modulus of continuity is given. Then, the equivalent theorem of these operators is studied.