Approximation properties for Baskakov-Kantorovich-Stancu type operators based on q- integers

TL;DR

This paper introduces a generalized form of Baskakov-Kantorovich-Stancu operators based on q-integers and studies their approximation capabilities, including convergence rates using weighted modulus of smoothness.

Contribution

It presents a novel generalization of classical operators using q-integers and analyzes their approximation properties and convergence rates.

Findings

Operators effectively approximate functions with quantifiable convergence rates

Weighted modulus of smoothness provides accurate estimates for convergence

Generalization extends applicability of classical approximation operators

Abstract

In this paper, we give an interesting generalization of the Stancu type Baskakov-Kantorovich operators based on the q-integers and investigate their approximation properties. Also, we obtain the estimates for the rate of convergence for a sequence of them by the weighted modulus of smoothness.