Approximation by q-Bernstein-Stancu-Kantorovich operators with shifted knots of real parameters

TL;DR

This paper introduces a new class of q-Bernstein-Kantorovich operators with shifted knots, analyzing their convergence and approximation properties in various function spaces using q-calculus techniques.

Contribution

It develops and studies the convergence of q-Bernstein-Kantorovich operators with shifted knots, extending classical approximation theory with new parameters and tools.

Findings

Operators converge uniformly on continuous functions

Quantitative estimates of approximation rate obtained

Degree of convergence linked to modulus of continuity

Abstract

Our main purpose of this article is to study the convergence and other related properties of q-Bernstein-Kantorovich operators including the shifted knots of real positive numbers. We design the shifted knots of Bernstein-Kantorovich operators generated by the basic q-calculus. More precisely, we study the convergence properties of our new operators in the space of continuous functions and Lebesgue space. We obtain the degree of convergence with the help of modulus of continuity and integral modulus of continuity. Furthermore, we establish the quantitative estimates of Voronovskaja-type.