Fractional integral inequalities for generalized convex functions

This thesis is on generalized Hermite-Hadamard type inequalities obtained with the help of generalized convex (F-convex) functions. The first part of this study, which has been prepared as five chapters, is an introduction and some definitions and theorems are given in the second part. Later, after the proof of Hermite-Hadamard inequality, the definition and some properties of F-convex functions are presented. The relationship between other convex function classes and F-Convex functions has been examined. The fractional integral operator and generalized fractional integral operator to be used in the main part of the thesis study are mentioned in the second section, respectively. In the third chapter, Hermite-Hadamard type inequalities for F-convex functions, including Riemann integral, Riemann-Liouville fractional Integrals and generalized fractional integrals, will be presented, respectively. The fourth part is the main part of the thesis. In this section, some new Hermite-Hadamard type inequalities for F-convex functions, including Riemann-Liouville Fractional Integrals and generalized fractional integrals, will be proved. In the fifth chapter, which is the last part of the thesis, some results and suggestions for further studies are given.