Local Approximation Properties for the New Type q-Stancu-Durrmeyer Operators

Abstract

In this article, new kind q-Stancu-Durrmeyer operators (or shortly q-SD operators) are defined. For these operators, first order and second order moments, U^{qa}_z(t^i,\\tau), are calculated for j=0,1,2. An estimation for the second order central moment U^{qa}_z(t-\\tau)^2 ,\\tau), is given. Furthermore, through the use of the second modulus of continuity, approximation properties of the q-SD operators in the local sense are examined and by using \\beta order Lipschitz kind maximal function, a direct estimation for the q-SD operators is given.