Approximation by α$$ \alpha $$‐Bernstein–Schurer operators and shape preserving properties via q$$ q $$‐analogue
Md. Nasiruzzaman, A. F. Aljohani
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.
Topics & Concepts
MathematicsModulus of continuityLipschitz continuityConvexityMonotonic functionType (biology)Alpha (finance)Pure mathematicsMathematical analysisDiscrete mathematicsStatisticsBiologyPsychometricsEconomicsEcologyConstruct validityFinancial economicsApproximation Theory and Sequence SpacesMathematical Approximation and IntegrationMathematical functions and polynomials