Convergence of B´ezier type (λ, q)-Bernstein-Kantorovich Shifted knots operators

Abstract

This article presents the Kantorovich formulation of (λ, q)-Bernstein operators related by B´ezier basis functions using the features of shifted knots. We derive these operators’ convergence and other associated approximation features. We use the modulus of continuity to discuss the degree of convergence of our operators. Furthermore, we derive the approximation in Lipschitz spaces and provide several fundamental direct theorems. The Voronovskaja type asymptotic formulas and some graphical examples are also presented.