P-power log-convex function and its applications

Abstract In this paper, the concept of p-power log-convex function is introduced. Some properties and discriminant criterion of p-power log-convex function are shown. Some examples are given. Several integral inequalities for p-power log-convex functions are proved. As an application, an extended weighted average inequality is given. The p-power log-convexity of Gamma function is researched, and two exponential function expansion residual inequalities are given.