New inequalities and applications for some convex function classes

In this thesis, two different lemmas gathered for first degree and nth degree, in general, differentiable functions have been handled. With the help of these lemmas, new inequalities for some convex classes have been obtained. The first part was introductory part which contained the historical developments of convex functions and Inequality Theory, as well as, some information related to studies in literature. In the second part, definitions of convex function and some kinds of it has been explained, hierarchy between them has been mentioned, and some examples has been given. In the third part, some inequalities which are very important and common, also lemmas and theorems which are used in our thesis were given. In the fourth part, new inequalities have been constructed by dealing with firstly, a lemma gathered for nth degree, in general, differentiable functions, then a lemma gathered for first degree differentiable functions. Then some special cases of gathered inequalities put forward. Finally, by using these results, propositions have been given for some special means. Also it was observed that the gathered results were supported by the literature.