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 operatorsand Brenke polynomials and studies their approximation properties. We also prove quantitative Voronovskaya-typeresults and establish Gru¨ss–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 byillustrative graphics using MATLAB.