On approximation of unbounded functions by certain modified Bernstein operators

Abstract

We show that by a simple modification of the Bernstein operators one can obtain a polynomial approximation of unbounded functions which admit an asymptote at an end point of the interval and we give a typical example. We define a certain modulus of continuity which allow to give a quantitative result for the degree of approximation and to make more explicit the class of functions which can be approximate. Finally we show that these operators could be transformed in order to obtain linear positive operators for approximation of functions on interval $ [0, \infty) $. The scheme used in this paper is applicable in more general cases.