Bernstein-type Inequalities Preserved by Modified Smirnov Operator

TL;DR

This paper introduces a modified Smirnov operator that preserves Bernstein-type inequalities, extending classical inequalities like those of Bernstein, Erdős, Lax, Ankeny, and Rivlin.

Contribution

It presents a new modified Smirnov operator and proves that it preserves several classical Bernstein-type inequalities, generalizing existing results.

Findings

Bernstein-type inequalities are preserved by the modified operator

Generalizations of classical inequalities are established

The results extend the applicability of these inequalities to new operator contexts

Abstract

In this paper, we consider a modified version of Smirnov operator and obtain some Bernstein-type inequalities preserved by this operator. In particular, we prove some compact generalizations of the well-known inequalities of Bernstein, Erd\"{o}s and Lax, Ankeny and Rivlin and others.