Inequalities for log-convex functions via three times differentiability

TL;DR

This paper develops new integral inequalities for third derivatives of log-convex functions, providing applications to quadrature error estimates and extending classical inequalities like Hermite-Hadamard.

Contribution

It introduces novel Hermite-Hadamard type inequalities for third derivatives of log-convex functions, with applications to numerical integration error bounds.

Findings

New integral inequalities for third derivatives of log-convex functions

Applications to midpoint quadrature error estimation

Extension of classical Hermite-Hadamard inequalities

Abstract

In this paper, we obtain some new integral inequalities like Hermite-Hadamard type for third derivatives absolute value are log-convex. We give some applications to quadrature formula for midpoint error estimate.