Some Approximation Properties of New Kind of Baskakov-Schurer-Szasz Operators

Abstract

This paper introduces a new class of parametric Baskakov-Schurer-Szasz operators based on sequences of continuous functions on [0, infinity). These operators extend the classical Baskakov-Schurer-Szasz framework by incorporating a novel parameter and function sequence. We establish a Korovkin-type theorem, prove a Gruss-Voronovskaya-type result, and determine the rate of convergence. Additionally, we analyze these generalizations within weighted spaces. The final section is dedicated to proving shape-preserving properties, demonstrating that our results encompass the classical operators as a special case.