Improvement of Jensen, Jensen-Steffensen's, and Jensen's functionals related inequalities for various types of convexity

TL;DR

This paper enhances inequalities involving Jensen, Jensen-Steffensen, and Jensen functionals for different convexity types, including uniformly convex, phi-convex, and superquadratic functions, providing tighter bounds and improved results.

Contribution

It introduces improved inequalities for Jensen-type functionals tailored to various convexity classes, extending existing theoretical frameworks.

Findings

Derived tighter bounds for Jensen-related inequalities.

Extended inequalities to superquadratic and phi-convex functions.

Provided theoretical improvements over classical Jensen inequalities.

Abstract

In this paper we deal with improvement of Jensen, Jensen-Steffensen's and Jensen's functionals related inequalities for uniformly convex, phi-convex and superquadratic functions.