The abstraction of the concept of convexity

Our aim in this theisis is to make a kind of literature search on the abstraction of convex term, to examine convex classes, revealed untill this time and to produce ideas about new convex classes by identifying the relationship between them. In this thesis, a detailed examination and discussion of the concept of B-convexity was given. In this study we have done, firstly we focused on the topological definitions and teorems and we make literatüre search about convex sets and basics of convex functions, together. With the identificion methods for abstraction of convexity were mentioned and necessary basic definitions and theorems in this field were given. A literature rewiev was conducted for different convexity classes and the hierarchy of some convex functions was expressed by given definition of each convexcity class. B-convexcity which are abstract convexity concepts were discussed and examined, B-convex sets, functions and properties are given. In addition, examples were found for B-convex and non B-convex function examples in R_+^2were found and the relationship between classical convex functions and B-convex function class was examined throuhg these examples. Besides that Elementary functions family of univariate B-convex function were found and some properties of univariate B-convex function were examined through this family functions.