Some Integral Inequalities For Functions Whoose Second Derivatives Are $\varphi$-Convex By Using Fractional Integrals

TL;DR

This paper develops new fractional integral inequalities that generalize classical inequalities like Hermite-Hadamard, Simpson, and Ostrowski for functions with second derivatives that are -convex, expanding the theoretical framework of inequality analysis.

Contribution

It introduces novel fractional integral inequalities for -convex functions' second derivatives, extending classical inequalities to a broader function class.

Findings

Derived generalized Hermite-Hadamard inequalities

Extended Simpson inequalities using fractional integrals

Provided Ostrowski type inequalities for -convex functions

Abstract

In this paper, we obtain new estimates on generalization of Hermite-Hadamard, Simpson and Ostrowski type inequalities for functions whose second derivatives is $\varphi$-convex via fractional integrals.