Weighted approximation by the family of generalized Sampling Durrmeyer operators

This thesis consists of five chapters. In the first chapter, preliminary information about approximation theory and sampling theory which is an important branch of approximation theory, is given. In the second chapter, the basic concepts and notations which are appropriate for the mathematical terminology used in the thesis are given. In the third chapter of the thesis, general concepts and properties of kernel functions, weighted continuous spaces of function and weighted modulus of continuity are given. In the fourth chapter, which forms the original part of the thesis, the local and global approximation results of the family of sampling Durrmeyer type operators in weighted continuous function spaces are examined and pointwise and uniform convergence results are obtained. In addition, the rate of convergence has been investigated via weighted modulus of continuity. Finally, a Voronovskaja type theorem is presented in order to obtain an upper estimate for this convergence. In this part numerical examples that are supporting the theoretical results are also presented. In the last chapter of the thesis the results are discussed.