Integral inequalities on the coordinates for exponentially convex functions

In this thesis, some exponentially convex functions of different types are examined on the rectangular region and various integral inequalities are obtained for these functions on the coordinates. The first chapter includes a brief historical overview of convex functions and inequality theory, and information about existing studies in the literature is given. In the second and third chapters, adetailed literature study has been made for convex functions and exponentially convex functions. In the fourth chapter, firstly, exponentially convex functions and different types of exponentially convexity are defined and their properties are proved. Then, some integral inequalities obtained as a result of multiplication of exponentially convex functions are obtained and new inequalities are obtained by using two lemmas existing in the literature. Finally, two new lemmas are proved and new theorems are obtained.