Some generalization methods of the concepts of convex set and convex function

Our aim in this thesis is to give the main generalization methods of convexity and related examples. In this thesis, first of all, the generalization methods of classical convex sets based on some properties such as separation, intersection, convex hull are mentioned and examples are presented. Later, the generalization methods of classical concept of convex function, some features and concepts of classical convex functions (a function convex functions based on some properties such as being supremum of a certain set of functions, convex hull for functions are given and related examples are presented. This thesis study consists of five chapters. In the first section of the thesis, a brief history of the concept of convexity is explained. In the second section of the thesis, general information about the sources used in the thesis is given. In the third section, basic definitions are given. The fourth section consists of three parts. The first part is about some generalization methods of convex sets. The second part is about some generalization methods of convex functions. The last part is about the conditions that can not fall into these two categories. For these three conditions, some examples are presented. In the fifth section, results and suggestions are given.