A short note on q-analogue of modified Stancu-Beta operators

TL;DR

This paper introduces modified q-Stancu-Beta operators, investigates their statistical approximation properties, and establishes their convergence rates, demonstrating they perform at least as well as classical operators.

Contribution

The paper develops and analyzes modified q-Stancu-Beta operators, providing new statistical approximation theorems and convergence rate estimates.

Findings

Operators exhibit at least as fast convergence as classical counterparts.

Statistical approximation theorems are established using Korovkin's theorem.

Rates of convergence are quantified via modulus of continuity and Lipschitz functions.

Abstract

This paper deals with the modified q-Stancu-Beta operators and we have investigated the statistical approximation theorems for these operators with the help of the Korovkin type approximation theorem. We have also established the rates of statistical convergence by means of the modulus of continuity and the Lipschitz type maximal function. Our results show that the rates of convergence of our operators are at least as fast as the classical Stancu-Beta operators.