Radical Convex Functions

TL;DR

This paper introduces radical convex functions, a new class with stronger convexity properties, providing novel bounds and applications in inequalities and analysis.

Contribution

It defines radical convex functions and explores their properties, establishing new bounds and applications in classical inequalities.

Findings

Radical convex functions are bounded above by new curves.

Applications to Jensen, Hermite-Hadamard, and integral inequalities.

Demonstrates stronger convexity behavior leads to improved bounds.

Abstract

In this article, we further explore convex functions by revealing new bounds, resulting from stronger convexity behavior. In particular, we define the so called radical convex functions and study their properties. We will see that such convex functions are bounded above by new curves, rather than straight lines. Applications including discrete and continuous Jensen inequalities, subadditivity behavior, Hermite-Hadamard and integral inequalities will be presented.