Some inequalities for differentiable convex functions with applications

TL;DR

This paper introduces new integral inequalities for differentiable convex functions using classical inequalities, and applies these results to compare special means, advancing the mathematical understanding of convex analysis.

Contribution

It establishes a novel identity for differentiable functions and derives new integral inequalities for convex functions, with applications to special means.

Findings

Derived a new identity for differentiable functions.

Obtained integral inequalities for convex functions.

Applied inequalities to compare special means.

Abstract

In this paper, the Authors establish a new identity for differentiable functions. By the well-known H\"older and power mean inequality, they obtain some integral inequalities related to the convex functions and apply these inequalities to special means.