Approximation by sampling type operators and applications to image processing

This thesis consists of six sections. The first section is reserved for introduction. The second section the sources used in writing the thesis are presented. In the third section the required basic notations and concepts are introduced and auxiliary results are presented. In the fourth section, the first results obtained by sampling type series in weighted spaces are stated without proof. The fifth section examines the convergence properties of modified sampling type operators, which are the main results of this thesis. In the last section, while graphical and numerical tables are presented for the newly introduced operator families, applications of bivariate modified sampling Kantorovich operators to image processing are also presented. In the relevant applications, the new operator families are compared with the classical ones and the results are presented.