Some inequalities of the Edmundson-Lah-Ribaric type for 3-convex functions with applications

TL;DR

This paper establishes new inequalities of Edmundson-Lah-Ribaric type for positive linear functionals and 3-convex functions, with applications to divergence measures, convex functions, and means, supported by examples including Zipf-Mandelbrot law.

Contribution

It introduces novel inequalities for 3-convex functions and positive linear functionals, extending existing mathematical frameworks and applying them to divergence functionals and means.

Findings

Derived Edmundson-Lah-Ribaric inequalities for 3-convex functions.

Applied inequalities to generalized f-divergence and Zipf-Mandelbrot law.

Constructed families of exponentially convex functions and Stolarsky-type means.

Abstract

In this paper we derive some Edmundson-Lah-Ribari\v{c} type inequalities for positive linear functionals and 3-convex functions. Main results are applied to the generalized f-divergence functional. Examples with Zipf Mandelbrot law are used to illustrate the results. In addition, obtained results are utilized in constructing some families of exponentially convex functions and Stolarsky-type means.