Hasan Barsam - Department of Mathematics, Faculty of Science, University of Jiroft, P.O. Box ۷۸۶۷۱-۶۱۱۶۷, Jiroft, Iran
Yamin Sayyari - Department of Mathematics, Sirjan University of Technology, Sirjan, Iran
Somayeh Mirzadeh - Department of Mathematics, University of Hormozgan, P.O. Box ۳۹۹۵, Bandar Abbas, Iran

In recent years, many researches have been done on the tgs-convex functions and their applications. In this article, we present some properties of the tgs-convex functions by interesting examples. Then we investigate the non-positive property of the tgs-convex functions. Also, we derive types of the Jensen’s inequality for the tgs-convex functions and obtain several inequalities with respect to the Jensen’s inequality. Finally, we give some applications of these inequalities.

Jensen’s inequality, tgs-convex function, Global bounds