Lower and Upper Bounds for ‘Useful’ Jensen Functional Convexity

Abstract

In the present paper, we will study the class of convex functions and emphasized certain basic conclusions related to the Jensen functional and its behavior in the setting of the convex function due to the scarcity of literature on the subject. The Jensen functional has been studied under a variety of assumptions, including strong convexity, quasiconvexity, and convexity, quasiconvexity. We present some new improvements on lower and upper bounds for the ‘useful’ Jensen functional in this paper. To explain the idea of a strongly convex function, we utilize a combination of old and recent results.