Fractional integral inequalities for B-convex functions

One of the subfield of convex analysis, which is one of the important areas of mathematics, is abstract convex analysis. In this thesis, primarily convex analysis and abstract convex analysis information are given mainly. Afterwards, abstract convexity types and B-convexity to be studied are mentioned. Then, the fractional integral types and the generalized Riemann-Liouville fractional integral to be studied are introduced. Hermite-Hadamard inequalities via these fractional integral operators are also included in the thesis. In this thesis, two items are mentioned as the main research findings. The first would be to prove a trapezoidal inequality for a function whose absolute value of derivative is B-convex. The second one is to express the Hermite-Hadamard inequality using the generalized Riemann-Liouville fractional integral for B-convex functions. Besides, some applications of these inequalities are given finally.