On Generalized Strongly Convex Functions and Unified Integral Operators

In this paper, we define a strongly exponentially α , h − m -convex function that generates several kinds of strongly convex and convex functions. The left and right unified integral operators of these functions satisfy some integral inequalities which are directly related to many unified and fractional integral inequalities. From the results of this paper, one can obtain various fractional integral operator inequalities that already exist in the literature.

Some norm and operator inequalities to improved AM-GM inequality with Specht’s ratio

In this paper, we present a refinement of the well-known arithmetic-geometric mean inequality. As application of our result, we obtain an operator inequality. We give an improvement of the inequality presented by Kittaneh for the numerical radius.