A Computational Analysis of Error Bounds for Novel α-Baskakov–Kantorovich Operators and Graphical Representation

This study introduces a novel family of hybrid Kantorovich-type operators for the Baskakov–Schurer–Stancu class, integrated with a shape parameter α∈0,1. We establish fundamental estimates and evaluate both the rate of convergence and the order of approximation utilizing the Korovkin theorem and the modulus of smoothness. Local approximation properties are further explored via Peetre’s K-functional. Numerical simulations and graphical analyses demonstrate that varying the shape parameter significantly improves approximation accuracy, confirming the practical efficacy of the proposed operators.