INEQUALITY ESTIMATE ON DURRMEYER TYPE OPERATORS

Abstract

In the present paper, we define a new Bezier variant of Durrmeyer type operators, which is a class of linear positive operators and study the rate of approximation for functions of bounded variation. For particular values our operators reduce to modified Bernstein polynomials, Baskakov Durrmeyer type operators and Szasz Durrmeyer operators. Our results extend and improve the results of Guo [J. Approx. Theory 51 (1987), 183-192] and Zeng and Chen [J. Approx. Theory 102 (2000), 1-12]  etc.