On the generalization some intgeral inequalities and their applications

TL;DR

This paper derives a general integral identity for convex functions, establishes new inequalities of Simpson and Hermite-Hadamard types for functions with convex derivatives, and applies these results to special means of real numbers.

Contribution

Introduces a new integral identity and novel inequalities of Simpson and Hermite-Hadamard types for convex functions and their derivatives.

Findings

New integral identity for convex functions

New inequalities of Simpson and Hermite-Hadamard types

Applications to special means of real numbers

Abstract

In this paper, a general integral identity for convex functions is derived. Then, we establish new some inequalities of the Simpson and the Hermite-Hadamard's type for functions whose absolute values of derivatives are convex. Some applications for special means of real numbers are also provided.