Hg-convex functions

In this thesis, a new function class, named Hg-convex function is identified. Some new Hermite-Hadamard typed simple inequalities are given. In the first part of the thesis, introductory informations about inequality theory, history of convex functions and convexity take part respectively. In the second part of the thesis basic notions, definitions and theorems necessary for theoretical foundations of the thesis are given and also the relations of Ag-convex function classes with each are transferred by the literature study. In the third part, theorems that include classic inequalities used in thesis study, their proofs and some inequalities that constitute that theoretical basic of this study are included. In the forth part, with the definition of a new function class named Hg-convex function, the relation of the function class with the literatüre is given, some algebraic properties of this class of function are examined. And then HermiteHadamard type fort he class of Hg-convex functions with the help of identity in the literature, some new inequalities have been archieved. Keywords: Convexity, Hermite-Hadamard Inequality, Integral Inequalities, Harmonic Convex Functions, Hg-convex functions