Gg-convex functions

In this thesis, a new function class called Gg-convex functions is defined. Some new Hermite-Hadamard type inequalities are given. The inequality information in the first part of the thesis is an introduction to the history of the convex function and convexity. In the second part, the basic concepts, definitions and theorems required for the theoretical foundations of the thesis are given, and the relationship between Agconvex function classes is explained, supported by the literature study. In the third chapter, the theorems including classical inequalities used in the thesis, their proofs and some inequalities that form the theoretical basis of this study are given. In the fourth chapter, with the definition of a new function class named Gg-convex function, the relationship of the function class with the literature is given, some algebraic properties of this class of functions are examined, and then, with the help of an identity in the literature, some new Hermite-Hadamard type for the class of Ggconvex functions. inequalities have been found. Keywords: Convexity, Hermite-Hadamard Inequality, Integral Inequalities, Ggconvex functions, Ag-convex functions