Kantorovich-Stancu type (α,λ,s) - Bernstein operators and their approximation properties

Nezihe Turhan, Faruk Özger and Mohammad Mursaleen

Mathematical and Computer Modelling of Dynamical Systems, 2024, vol. 30, issue 1, 228-265

Abstract: In this study, we establish a new class of Kantorovich-Stancu type $\left({\alpha ,\lambda ,s} \right) - $α,λ,s−Bernstein operators via an adaptation of Bézier bases which are formulated with the inclusion of the shape parameters $\lambda \in \left[{ - 1,1} \right]$λ∈−1,1, $\alpha \in \left[{0,1} \right]$α∈0,1, and a positive parameter $s.$s. First, we present a uniform convergence result for these operators and, subsequently, examine the convergence properties by utilizing the weighted $B$B-statistical convergence notion. Furthermore, we estimate the rate of the weighted $B$B-statistical convergence of these operators. We conclude our work by providing a numerical example with explanatory graphs to show their approximation behaviours.

Date: 2024
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DOI: 10.1080/13873954.2024.2335382

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