On statistical approximation properties of $q$-Baskakov-Szasz-Stancu operators

TL;DR

This paper investigates the statistical approximation capabilities of a generalized class of Baskakov-Szász-Stancu operators based on q-integers, providing convergence rates and approximation properties.

Contribution

It introduces a Stancu type generalization of Baskakov-Szász operators using q-integers and analyzes their statistical approximation properties.

Findings

Established statistical and weighted statistical approximation properties.

Derived rates of statistical convergence using modulus of continuity.

Analyzed approximation behavior with Lipschitz type maximal functions.

Abstract

In the present paper, we consider Stancu type generalization of Baskakov-Sz\'{a}sz operators based on the q-integers and obtain statistical and weighted statistical approximation properties of these operators. Rates of statistical convergence by means of the modulus of continuity and the Lipschitz type maximal function are also established for operators.