On a Family of Parameter-Based Bernstein Type Operators with Shape-Preserving Properties

Abstract

This article aims to introduce a new linear positive operator with a parameter. Our focus lies in analyzing the distinct characteristics and inherent properties exhibited by this operator. Additionally, we provide a proof of the convergence rate and present a revised version of the Voronovskaja theorem specifically tailored for this newly defined operator. Furthermore, we provide an upper bound for the error according to the modulus of continuity. Finally, the preservation of monotonicity and convexity by the operator is being investigated.