Jensen's Inequalities in Two and Three Dimensions

TL;DR

This paper extends Jensen's inequality to two and three dimensions, providing new symmetric inequalities in multivariable analysis with broad applications.

Contribution

It introduces generalized Jensen's inequalities in two and three dimensions, expanding the scope of classical convexity-based inequalities.

Findings

Established new symmetric inequalities in $ extbf{R}^{2}$ and $ extbf{R}^3$

Demonstrated applications in various analysis problems

Generalized Jensen's inequality to higher dimensions

Abstract

We prove certain type symmetric inequalities in $\textbf{R}^{2}$ and $\textbf{R}^3$, that ocur in many problems of analysis. These inequalities are generalizations of the Jensen's inequality from one variable to two and three variables