Approximation for q-Chlodowsky operators via statistical convergence with respect to power series method

This thesis consists of five chapters. The first chapter is devoted to the introduction. In the second chapter, by recalling the concepts of statistical convergence and statistical convergence with respect to power series method, basic definitions, theorems and well known results which we need throughout the thesis, also definitions of linear positive operators, modulus of continuity and q-analysis and some of their important properties are given. In the third chapter, q-Chlodowsky operators are defined, some approximation properties of these operators are examined and some approximation results obtained with classical convergence are given. The original results of this thesis are included in the fourth chapter. In this chapter, the approximation properties of Chlodowsky operators defined by q-analysis are examined with the use of statistical convergence with respect to power series method which is not included by previously known methods, the rate of convergence is obtained and an example to these original results is given. In the last chapter, the original results obtained in during the thesis are evaluated and its contribution to the literature is mentioned.