Approximation by ?-Baskakov-Kantorovich Operators

Abstract

In this paper, we introduce a new family of Baskakov-Kantorovich operators that depend on a function psi. We compare these new psi-Baskakov-Kantorovich operators with the classical Baskakov-Kantorovich operators to evaluate their approximation results. Our analysis shows that these new operators provide better approximation results across the entire interval [0,infinity) We demonstrate their uniform convergence in weighted spaces and determine their convergence rates using both first- and second-order moduli of continuity. We also prove that these operators preserve shape-preserving properties. We support our findings with graphical and numerical examples.