Hermite-hadamard-fejer inequality for B-1 -convex functions

Theory of Inequalities is one of the most important and useful application areas of convex functions. The inequality to be discussed in the thesis is the Hermite-Hadamard-Fejer inequality, which plays a critical role in solving various mathematical problems. In this thesis, studies have been carried out on obtaining the Hermite-Hadamard-Fejer inequality for B-1-convex functions, which is a type of abstract convexity. Firstly, the thesis includes definitions and theorems for B-1-convex sets and functions. In this section, some examples of B-1-convex sets and functions are also added to the literature. In the next section, the general form of the Hermite-Hadamard-Fejer inequality for B-1-convex functions is proven. Then, different inequalities are proved by introducing special conditions for functions on this general form and their applications are given.