On a convexity property

TL;DR

This paper explores a convexity property of continuous convex functions, deriving a generalized Hermite-Hadamard inequality and discussing its implications for convex analysis.

Contribution

It introduces a new convexity property and generalizes the Hermite-Hadamard inequality for continuous convex functions.

Findings

Established a new convexity property.

Derived a generalized Hermite-Hadamard inequality.

Discussed implications for convex function analysis.

Abstract

In this article we proved an interesting property of the class of continuous convex functions. This leads to the form of pre-Hermite-Hadamard inequality which in turn admits a generalization of the famous Hermite-Hadamard inequality. Some further discussion is also given.