Sercan Turhan - Department of Mathematics, University of Giresun, Giresun, Turkey
Mehmet Kunt - Department of Mathematics, University of Karadeniz Technical, Trabzon, Turkey
İmdat İşcan - Department of Mathematics, University of Giresun, Giresun, Turkey

This article deals with the different classes of convexity and generalizations. Firstly, we reveal the new generalization of the definition of convexity that can reduce many order of convexity. We have showed features of algebra for this new convex function. Then after we have constituted Hermite-Hadamard type inequalities for this class of functions. Finally the identity has been revealed for its by us and by using this identity, then theorems and corollaries have been obtained.

M_{varphi }A-convex function, Hermite-Hadamard type inequality, GA-convex function, convex function, harmonically convex function