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

Abstract

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