On q-analogue of modified Kantorovich-type discrete-Beta operators

TL;DR

This paper introduces a Stancu type generalization of q-analogue Kantorovich discrete Beta operators, providing new theoretical results on their approximation properties and error bounds.

Contribution

It presents a novel generalization of q-Beta operators and establishes their asymptotic behavior and error estimates in approximation theory.

Findings

Established asymptotic formulas for the generalized operators

Derived error estimates using modulus of continuity

Enhanced understanding of q-analogue discrete Beta operators

Abstract

The present paper deals with the Stancu type generalization of the Kantorovich discrete $q$-Beta operators. We establish some direct results, which include the asymptotic formula and error estimation in terms of the modulus of continuity and weighted approximation.