Various integral inequalities on the co-ordinates via Riemann integrals

In this thesis, convex functions are examined on the rectangular region and various integral inequalities are obtained for these functions in coordinates. The first chapter contains a brief historical overview for convex functions and inequality theory, and information about the existing studies in the literature is given. In the second chapter, basic definitions and concepts for convex functions are included, and the relationship between convex function classes is mentioned. Basic definitions and concepts related to convex functions in coordinates, various integral inequalities and proof methods for these function classes are given in the third chapter. Then, in this section, detailed literature information for integral inequalities in coordinates is presented. In the fourth chapter, firstly, a new integral identity is presented, and then with the help of this equation, results regarding new integral inequalities for convex functions on the rectangular region are obtained.