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

Abstract

ABSTRACTIn this study, we establish a new class of Kantorovich-Stancu type [Formula: see text]Bernstein operators via an adaptation of Bézier bases which are formulated with the inclusion of the shape parameters [Formula: see text], [Formula: see text], and a positive parameter [Formula: see text] First, we present a uniform convergence result for these operators and, subsequently, examine the convergence properties by utilizing the weighted [Formula: see text]-statistical convergence notion. Furthermore, we estimate the rate of the weighted [Formula: see text]-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