MKZ type operators providing a better estimation on [1/2,1)

Abstract

In the present paper, we introduce a modification of the Meyer-Konig and Zeller (MKZ) operators which preserve the test functions fo(x) = 1 and f(2)(x) = x(2), and we show that this modification provides a better estimation than the classical MKZ operators on the interval [ 1/2: 1) with respect to the modulus of continuity and the Lipschitz class functionals. Furthermore, we present the r-th order generalization of our operators and study their approximation properties.