Improved eigenvalue inequalities via two major subclasses of superquadratic functions

TL;DR

This paper introduces new eigenvalue inequalities by exploiting the properties of two main subclasses of superquadratic functions, refining existing bounds for convex functions and deriving new inequalities for other function types.

Contribution

It presents novel eigenvalue inequalities based on the classification of superquadratic functions into concave decreasing and convex increasing subclasses.

Findings

Refined eigenvalue inequalities for convex superquadratic functions.

Derived complementary inequalities for concave decreasing superquadratic functions.

Provided illustrative examples demonstrating the inequalities.

Abstract

There exist two major subclasses in the class of superquadratic functions, one comprises concave and decreasing functions, while the other consists of convex and monotone increasing functions. Leveraging this distinction, we introduce eigenvalue inequalities for each case. The characteristics of these functions allow us to advance our findings in two ways: firstly, by refining existing results related to eigenvalues for convex functions, and secondly, by deriving complementary inequalities for other function types. To bolster our claims, we will provide illustrative examples.