On the generalized convexity and concavity

TL;DR

This paper investigates the properties of convexity and concavity of real functions relative to classical means, proving a conjecture by Bruce Ebanks and expanding the understanding of generalized convexity.

Contribution

It introduces a new framework for analyzing convexity and concavity with respect to classical means, confirming a previously posed conjecture.

Findings

Proved a conjecture on generalized convexity and concavity.

Established new relationships between functions and classical means.

Enhanced theoretical understanding of function properties in mathematical analysis.

Abstract

In this paper, authors study the convexity and concavity properties of real-valued function with respect to the classical means, and prove a conjecture posed by Bruce Ebanks in \cite{e}.