Approximation by α$$ \alpha $$‐Bernstein–Schurer operators and shape preserving properties via q$$ q $$‐analogue
Copyright policy )Approximation by α$$ \alpha $$‐Bernstein–Schurer operators and shape preserving properties via q$$ q $$‐analogue
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.
- University of Tabuk Saudi Arabia
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Schurer operators, shape preserving property, global approximation, \(q\)-integers, Voronovskaja-type theorem, Approximation by positive operators, Lipschitz-maximal function, Rate of convergence, degree of approximation, Bernstein operators
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Schurer operators, shape preserving property, global approximation, \(q\)-integers, Voronovskaja-type theorem, Approximation by positive operators, Lipschitz-maximal function, Rate of convergence, degree of approximation, Bernstein operators
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