Approximation by ψ$$ \psi $$‐Baskakov‐Kantorovich Operators.

Mathematical Methods in the Applied Sciences. Jun2025, p1. 11p. 5 Illustrations.

ABSTRACT In this paper, we introduce a new family of Baskakov‐Kantorovich operators that depend on a function ψ$$ \psi $$. We compare these new ψ$$ \psi $$‐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,∞)$$ \left[0,\infty \right) $$. 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. [ABSTRACT FROM AUTHOR]

*Approximation error, *Function spaces, *Continuous functions, *Empirical research

Copyright of Mathematical Methods in the Applied Sciences is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)