Approximation by ?-Baskakov-Kantorovich Operators - Aktuglu, Hueseyin; Kara, Mustafa; Baytunc, Erdem (Wiley, 2025)
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.
Keywords: Baskakov operators; Baskakov-Kantorovich operators; modulus of continuity; polynomial approximation; rate of convergence; shape-preserving properties; uniform convergence