On a Converse of Generalized ‘Useful’ Jensen’s Inequality with Data Illustration

In the present communication, we give the converse of generalized ‘useful’ Jensen inequality and show that some recently reported inequalities are simple consequences of those results that have been established for a long time. We also include a new improvement of the proposed inequality of Jensen as well as changes to some associated outcomes, where generalized ‘useful’ converse of the Inequality of Jensen is presented and implementations related to it are given in the theory of information. Finally, it is shown with the help of numerical data that inequalities holds well both for convex and concave functions.