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

ABSTRACT

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

KEYWORDS:

• Statistical rate of convergence
• error analysis
• shape parameter

Acknowledgments

The authors have greatly benefitted from the constructive feedback of the editor and anonymous referees. Therefore, they express their gratitude for the valuable comments provided on the initial draft of this paper, which contributed to enhancing its presentation and readability.

Disclosure statement

No potential conflict of interest was reported by the author(s).