math. sci. appl. e-notes Mathematical Sciences and Applications E-Notes 2147-6268 Murat TOSUN 10.36753/mathenot.1847910 Approximation Theory and Asymptotic Methods Yaklaşım Teorisi ve Asimptotik Yöntemler On the Stancu Type of Novel Generalization of $\left(\lambda,\mu\right)$-Bernstein-Kantorovich Operators https://orcid.org/0000-0002-9195-9043 Bodur Murat KONYA TECHNICAL UNIVERSITY, FACULTY OF ENGINEERING AND NATURAL SCIENCES, DEPARTMENT OF BASIC ENGINEERING SCIENCES 02 26 2026 14 1 21 31 12 23 2025 02 24 2026 Copyright © 2013, Mathematical Sciences and Applications E-Notes 2013 Mathematical Sciences and Applications E-Notes

This study investigates the shape parameters $\lambda$ and $\mu$, a concept of contemporary interest due to their capacity to introduce considerable flexibility and enhance modeling possibilities within approximation theory. This paper mainly introduces novel generalized $(\lambda,\mu)$-Bernstein-Kantorovich-Stancu operators. We examine the approximation properties of these operators, establishing the order of approximation through classical methods, specifically utilizing the Lipschitz class and the second modulus of continuity. Finally, to substantiate our theoretical findings, we present comprehensive numerical and graphical illustrations.

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