APPROXIMATION PROPERTIES OF A KANTOROVICH TYPE OPERATOR

Abstract

This study has been prepared in the theory of approximation, which has an important place in the fields of application. In this paper, a modification of operators of the Gadjiev-Ibragimov type that preserves test functions will be described. The paper is about Kantorovich-type modification of a generalization of Gadjiev-Ibragimov operators. It is aimed to present a new materials to researchers who will conduct applied studies by examining the uniform convergence of this of the new operator in integral form, whose terms are functions defined on C[0,1]. Based on the Korovkin approximation theorem, properties of convergence for these operators and then some direct theorems will be given.The rate of convergence of these operators will be calculated with the help of the modulus of continuity by using the classical second order moments. By using the definition created by Ozarslan and Aktuglu, the approximation theorem for functions from the Lipschitz class will be given and the approximation properties of these modified operators in weighted spaces will also be examined. Also, properties of approximation will be demonstrated with graphics and numerical calculations using the Maple program.