Approximation by Modified Bivariate Bernstein-Durrmeyer and GBS Bivariate Bernstein-Durrmeyer Operators on a Triangular Region
Harun ÇİÇEK, Aydın İzgi
Abstract
In this paper, the approximation properties and the rate of convergence of modified bivariate Bernstein-Durrmeyer Operators on a triangular region are examined. Furthermore, definitions and some properties of modulus of continuity for functions of two variables are given. Voronovskaya and Gr\"{u}ss Voronovskaja type theorems are used to determine the order of approximation. The GBS (Generalized Boolean Sum) operator of Bivariate Bernstein-Durrmeyer type on a triangular region is studied. Lastly, some numerical examples are given and related graphs are plotted for comparison.
Topics & Concepts
Bivariate analysisMathematicsModulus of continuityRate of convergenceBernstein polynomialType (biology)Convergence (economics)Operator (biology)Order (exchange)Applied mathematicsPure mathematicsStatisticsTranscription factorBiologyEcologyEconomic growthBiochemistryFinanceEngineeringChannel (broadcasting)Electrical engineeringEconomicsGeneChemistryRepressorApproximation Theory and Sequence SpacesIterative Methods for Nonlinear EquationsMathematical functions and polynomials