Geometric-quadratic convex functions and integral inequlaties and applications concerning with second derivative of a functions

In this thesis, some new integral inequalities are handled and applications are given by applying different convexity classes to a lemma for second order differentiable functions which exist in the literatüre. Also geometric-quadratic convex function class is defined, lemmas, theorems and examples belong to this class are given. The first part is introductory part which includes information about the findings of the studies related convex functions and inequalities conducted until now. The second includes convex function concepts used in the thesis, the hierarchies among them, basic theorems and some special means of positive real numbers. In the third part, some theorems which are going to be used in the main part of the research are given. In the fourth part, firstly, some inequalities for functions whose second derivatives are (α,m)-convex, s- convex or quasi- convex are obtained and applications are given to some of the found inequalities, then geometric-quadratic convex function class is defined; lemmas, theorems and examples belong to this class are given. Most of the findings of this thesis were observed to be supported by the literature.