Approximation theorems for certain positive linear operators

Abstract

In this work we prove approximation theorems for certain positive linear operators via Ditzian-Totik moduli omega(2,phi) (f, .) of second order where the step-weights are functions whose squares are concave. The results obtained are applied to the q-Lupas-Bernstein operators, the omega, q-Bernstein operators and the convergence of the iterates of the q-Bernstein polynomials. (C) 2010 Elsevier Ltd. All rights reserved.