Some integral inequalties on geometric convex functions

In this thesis, some new integral inequalities have been given related to geometric- arithmetic convex and geometric-harmonic convex functions. In the first section, some informations have been given on convex analysis and inequality theory. In the second part, some definitions, basic concepts and fundamental results have been recalled. Third part of our study include integral inequalities that have been proved via geometic convex functions, previously. In the fourth section, new integral inequalities of Hadamard type have been established for functions whose absolute values of derivatives are geometric convex by using basic concepts and elemantery analysis techniques. Also, some new integral inequalities which involve product of several geometric convex functions have been proved. Finally, by choosing some special cases and examples, applicaitions have been given. In the last section, a short discussion has been achieved on our results. 2016, 59 pages Keywords: Convex functions, GA−convex function, GG−convex function, GH−convex function, Hermite-Hadamard inequality, Hölder inequality.