On a compound approximation operator of D.D. Stancu type

Abstract

In this note we consider a linear and positive compound approximation operator of D.D. Stancu type depending of several parameters; we give the expressions of this operator on the test functions, the conditions under which this operator converges to a given continuous function, an estimate of the order of approximation using the moduli of continuity and an integral representation of the remainder. Also, by using Stancu's method we find an expression for the remainder using divided differences of second order for a special case of this operator.