ON THE APPROXIMATION WITH AN IBRAGIMOV-GADJIEV TYPE OPERATOR

Abstract

This work is a study examining the approximation properties of an Ibragimov-Gadjiev type operator, which contains important visual and numerical information in the field of operator theory, which is one of the applied areas of mathematics. Approximation theory; it is based on approaching difficult and complex functions with simpler and workable functions whose properties are known. In this sense, many operators have been defined and found a place in different fields of mathematics and in solving the problems of daily life. For example, Bernstein operators are used to create a simulation of blood pressure. Contrary to the classical Ibragimov-Gadjiev operator, where derivative properties should be used, important properties of the operator are obtained by using the properties of the continuous functions and the sum formula. The described operator is a tool that researchers can use for applied studies on daily life. This operator, which is used to approximate the functions defined on C[0,A] in the literature; It has been generalized to provide suitable properties for test functions by making the bounded depends on the variable. Then, a kernel function for the operator is determined by providing the necessary properties to obtain the smooth convergence of each function in the space.Then, the speed of approach was calculated with the help of the modulus of continuity.The results obtained with graphics and tables are given in practice.