Bivariate extension of Durrmeyer operators by D. D. Stancu

Abstract

In this report, we review some basic definitions related to approximation theory. Then, we study some approximation properties and rate of convergence for certain bivariate linear positive operators. In chapter 1, we recall some linear positive operators in two variables I. e. Bernstein polynomials, Schurer-Stancu operators, Baskakov Kantorovich operators, and properties of the Baskakov-Kantorovich operators, Generalized Baskakov-Kantorovich operators, Durrmeyer operators etc. We review the main results for these operators. In chapter 2, we investigated the Bivariate extension of Durrmeyer operators by D. D. Stancu. We obtain auxiliary results for these operators. Then, we study the rate of convergence in terms of second order modulus of continuity, basic convergence theorem and asymptotic formula for these operators.