Hermite-Hadamard type integral inequalities and their applications for functions whose derivatives are in different types of convexity

In this thesis, new integral inequalities were gathered by investigating second degree and nth degree, in general, differentiable functions. The first part was introductory part which included the historical developments of convex functions and Inequality Theory, as well as, information related to studies in literature. In the second part, concepts of convex functions used in the thesis, the hierarchy between them, and some theorems were given. In the third part, some integral inequalities related to second degree and nth degree, in general, differentiable functions in literature were given. In the fourth part, on the other hand, a new lemma for second degree differentiable convex functions was found and some new inequalities were gathered by using this lemma and some applications were given with the results gathered from these inequalities. In addition, new inequalities were gathered by applying some convex function classes to a lemma in the literature for nth degree differentiable functions. It was observed that the obtained results were supported by the literature.