Approximation properties of a Kantorovich-type operator based on Charlier polynomials

In this thesis, Kantrovich-type generalization of generalized Szász operators including Charlier Polynomials is defined and some approximation properties are examined. This thesis consists of eight chapters. In the first chapter, two main problems in approximation theory and the main studies in this field are presented in historical order. In the second chapter, the basic concepts required for the thesis are given. In the third chapter, some important theorems of approximation theory are given. In the fourth chapter, Kantrovich-type generalized Szász operators containing Charlier Polynomials is defined, some approximation properties are examined and the central moments of the defined operator are calculated. In addition, the rate of convergence of the operator is detamined by mathematical tools. In the fifth chapter, a Voronovskaya-type theorem is constructed for the defined operator. In the sixth chapter the approximation properties of the defined operator are exanined in weighted space. In the seventh chapter, the approximation result obtained by using the first modulus of continuity is shown with two numerical examples. The results were obtained by using the Maple 2022 program. Finally, conclusions and recommendations are given in the eighth chapter.