Approximation by α$$ \alpha $$‐Bernstein–Schurer operators and shape preserving properties via q$$ q $$‐analogue

Abstract

Our work in this article is to construct the ‐ Bernstein–Schurer operators which includes the ‐integers. For these new operators, we discuss the shape preserving properties, namely, monotonicity and convexity. Next, we study the uniformly global approximation in terms of the Ditzian–Totik modulus of continuity and calculate the local direct estimate by Lipschitz‐maximal functions. In the last Voronovskaja‐type approximation theorems are also presented.