What question did this study set out to answer?

The aim is to explore the flexibility of shape parameters lambda and mu in improving approximation methodologies.

February 28, 2026Mathematical Sciences and Applications E-Notes0 citationsOpen Access

On the Stancu Type of Novel Generalization of (, ) -Bernstein-Kantorovich Operators

Key Points

The aim is to explore the flexibility of shape parameters lambda and mu in improving approximation methodologies.
Introduction of novel generalized (λ,μ)-Bernstein-Kantorovich-Stancu operators.
Examination of approximation properties using classical methods.
Utilization of the Lipschitz class and second modulus of continuity for analysis.
Comprehensive numerical and graphical illustrations to support findings.
Establishment of the order of approximation for the new operators.
Demonstration of improved modeling possibilities with the generalized operators.

Abstract

This study investigates the shape parameters and, 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 (, ) -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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