Quantitative Voronovskaya- and Grüss-Voronovskaya-type theorems by the blending variant of Szász operators including Brenke-type polynomials

Abstract

The present paper aims to investigate a class of linear positive operators by combining Szász-Jain operators and Brenke polynomials and studies their approximation properties. We also prove quantitative Voronovskaya-type results and establish Grüss-Voronovskaja-type theorem. Furthermore, we show the rate of convergence for Szász-Jain-Brenke operators to functions having derivative of bounded variation and not having derivative of bounded variation by illustrative graphics using MATLAB.