tgs-convex function

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.