Improvements of the integral Jensen inequality through the treatment of the concept of convexity of thrice differential functions

Abstract

Jensen's inequality, with its broad applications across various fields, presents an important subject for investigation and research. In this article, we introduce novel enhancements to Jensen's inequality by utilizing the convexity properties of a thrice differentiable function in the absolute sense. We conducted numerical experiments to compare our primary results with previously established findings. Additionally, we provided several applications of our major results to classical inequalities, means, and divergences.

Keywords

• convex function
• concave function
• jensen's inequality
• hölder inequality