eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2019-05-05 7 3 59 64 10.12691/tjant-7-3-1 TJANT2019731 article Mahir Kadakal mahirkadakal@gmail.com 1 Department of Mathematics, Faculty of Sciences and Arts, Giresun University, Giresun-Turkey In this study, we present a new definition of convexity. This definition is the class of strongly multiplicatively P-functions. Some new Hermite-Hadamard type inequalities are derived for strongly multiplicatively -functions. Some applications to special means of real numbers are given. Ideas of this paper may stimulate further research. http://pubs.sciepub.com/tjant/7/3/1/tjant-7-3-1.pdf Convex function multiplicatively P-function strongly multiplicatively P-function H?lder and Power-Mean Integral inequalities Hermite-Hadamard inequality