Inegalit\u{a}\c{t}i de tip Chebyshev-Gr\"uss pentru operatorii Bernstein-Euler-Jacobi

TL;DR

This paper develops Chebyshev-Grüss type inequalities for Bernstein-Euler-Jacobi operators, providing bounds on the difference between the operator's integral of a product and the product of integrals, using moments of the operators.

Contribution

It introduces new Chebyshev-Grüss inequalities tailored for Bernstein-Euler-Jacobi operators of both kinds, expanding the theoretical framework for these operators.

Findings

Derived Chebyshev-Grüss inequalities for BEJ operators.

Applied moments of operators to establish bounds.

Extended classical inequalities to new operator classes.

Abstract

The classical form of Gr\"{u}ss' inequality was first published by G. Gr\"{u}ss in 1935 and gives an estimate of the difference between the integral of the product and the product of the integrals of two functions. After that many variants of this inequality appeared in the literature. The aim of this paper is to consider some Chebyshev-Gr\"{u}ss-type inequalities and apply them to Bernstein-Euler-Jacobi (BEJ) operators of first and second kind. First and second moments of the operators are used to explain the situation.