Integral inequalities for convex functions based on means

In this thesis, integral inequalities have been given for convex functions based on means. In the first part of the study, definitions, theorems and examples for convex function classes have been placed. In the second part, a historical glance on the convexity and integral inequalities has been given, some integral equalities, integral inequalities that have been obtained via these equalities and integral inequalities of Hermite-Hadamard type, Ostrowski type and Simpson type for convex functions have been established. In the third part, new inequalities have been obtained for convex functions based on means via new integral equalities. The aim of this thesis is to search kinds of convexity based on means deeply and to obtain some integral inequalities for these classes of functions.