On approximation properties of Baskakov-Schurer-Szasz operators

TL;DR

This paper investigates the approximation capabilities of new Baskakov-Schurer-Szasz operators, including their convergence rates, weighted space behavior, q-analogues, and statistical properties, with improved error estimates.

Contribution

It introduces new Baskakov-Schurer-Szasz operators and analyzes their approximation properties, including q-analogues and statistical convergence, with enhanced error bounds.

Findings

Established convergence rates using moduli of smoothness

Analyzed weighted space convergence of the operators

Derived improved error estimates via King type approach

Abstract

In this paper, we are dealing with a new type of Baskakov-Schurer-Szasz operators (\ref{eq1}). Approximation properties of this operators are explored: the rate of convergence in terms of the usual moduli of smoothness is given, the convergence in certain weighted spaces is investigated. We study $q$-analogues of Baskakov-Schurer-Sz\'{a}sz operators and it's Stancu generalization. In the last section, we give better error estimations for the operators (\ref{eq2}) using King type approach and obtained weighted statistical approximation properties for operator (\ref{qb})