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Degree of Approximation for Bivariate Generalized Bernstein Type Operators

  • Tuncer Acar
  • Arun Kajla
Article

Abstract

In this paper we study an extension of the bivariate generalized Bernstein operators based on a non-negative real parameters. For these operators we obtain the order of approximation using Peetre’s K-functional, a Voronovskaja type theorem and the degree of approximation by means of the Lipschitz class. Further, we consider the Generalized Boolean Sum operators of generalized Bernstein type and we study the degree of approximation in terms of the mixed modulus of continuity. Finally, we show the comparisons by some illustrative graphics in Maple for the convergence of the operators to certain functions.

Keywords

GBS operators B-continuous function B-differentiable function mixed modulus of smoothness 

Mathematics Subject Classification

41A10 41A25 41A36 41A63 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsCentral University of HaryanaHaryanaIndia
  2. 2.Department of Mathematics, Faculty of ScienceSelcuk UniversitySelçukluTurkey

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