Approximation by Modified Bivariate Bernstein-Durrmeyer and GBS Bivariate Bernstein-Durrmeyer Operators on a Triangular Region

Authors : Harun Çiçek, Aydın Izgi

Pages : 135-144

Doi:10.33401/fujma.1009058

View : 20 | Download : 8

Publication Date : 2022-06-01

Article Type : Research

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.
Keywords : Approximation properties, GBS operators, Modulus of continuity, Voronovskaja and Gr"{u}ss Voronovskaja theorem