What question did this study set out to answer?

The aim is to explore the approximation properties of the Kantorovich modified Schurer type (λ,q)-Bernstein operators.

February 14, 2026Open Access

Approximation Associated with Kantorovich Version of Bézier (λ,q)–Bernstein–Schurer Operators

MNMd. NasiruzzamanUniversity of Tabuk MFMohammad FaridQassim University HÇHarun ÇİÇEKUniversity of Žilina

Key Points

The aim is to explore the approximation properties of the Kantorovich modified Schurer type (λ,q)-Bernstein operators.
Presentation of Kantorovich modification of Schurer (λ,q)-Bernstein operators.
Application of Korovkin's theorem for approximation properties.
Analysis of convergence for functions in Peetre's K-functional and Lipschitz maximum.
Establishment of multiple local and global approximation properties.
Calculation of convergence properties with classical and second-order moduli of continuity.
Graphical and numerical results support the theoretical findings.

Abstract

In the present paper, the Kantorovich modification of the Schurer type of (λ,q)-Bernstein operators, which are associated by the shape parameter −1≤λ≤1 and the Bézier basis function, is presented. Using Korovkin’s theorem, we establish several local and global approximation properties. Lastly, we calculate the convergence properties for the functions that belong to Peetre’s K-functional and Lipschitz maximum by using the classical modulus of continuity and second-order modulus of continuity. In the last section, graphical and numerical analysis are studied.

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