Hermite-Hadamard-Fejer type inequalities for B-Convex function

Convex analysis is one of the popular field in recents. In this thesis, an application of inequality on the abstract convexity that is a subfield of convex analysis is made. B-convexity is the generalized convexity type and Hermite-Hadamard-Fejer type inequality is the inequality examined in the thesis. Thus, in the thesis, expression and applications of a more general inequality for B-convex functions, studied on applications to the optimization, economy and different inequalities until now, is given.In this thesis, first, some new examples about B-convex sets and functions are given. Also, a new form of the Hermite-Hadamard-Fejer inequality for B-convexity is expressed. Then, different theorems are improved by putting special conditions on the handling functions for the inequality. Examples specialized on given conditions are examined and theorems for the functions, which are B-convex or are not B-convex, are proven. Finally, desired inequalities given more proper approaches are obtained.