Approximation Theorems by Meyer-Konig and Zeller Type Operators

Abstract

This paper is mainly connected with the approximation properties of Meyer-Konig and Zeller (MKZ) type operators. We first introduce a general sequence of MKZ operators based oil q-integers and then obtain a Korovkin-type approximation theorem for these operators. We also compute their rates of convergence by means of modulus of continuity and the elements of Lipschitz class functionals. Furthermore, we give an rth order generalization of our operators in order to get some explicit approximation results. (C) 2008 Elsevier Ltd. All rights reserved.