Some generalizations of convex functions and integral inequalities

The first part of this thesis, which consists of four main chapters, includes information about the historical process of convex functions, fractional analysis and Hermite-Hadamard inequality. In the second part, firstly different classes of convex functions and Hermite-Hadamard type inequalities are given. Then some important inequalities, fractional integral operators, special functions and identities are given. In the third part, the findings section, firstly n-fractional polynomial p-convex function class is defined and Hermite-Hadamard type inequalities are obtained. Then n-fractional polynomial s-type convex function class is defined and respectively Hermite-Hadamard type inequalities and Ostrowski type inequalities are obtained. Finally, the Hermite-Hadamard inequality for (M_φ,M_ψ)-convex functions and some properties of this class of functions are presented. In the last part, results and suggestions are given.