On the Integral inequalities for mappings whose second derivatives are convex and applications

TL;DR

This paper develops new integral inequalities for twice differentiable convex mappings and applies them to improve numerical integration rules and analyze special means of real numbers.

Contribution

It introduces novel inequalities for twice differentiable convex functions and extends their application to numerical integration and mean inequalities.

Findings

New inequalities for twice differentiable convex functions

Enhanced midpoint, trapezoid, and perturbed trapezoid rules

Applications to inequalities involving special means

Abstract

In this paper, we establish several new inequalities for some twice differantiable mappings. Then, we apply these inequalities to obtain new midpoint, trapezoid and perturbed trapezoid rules. Finally, some applications for special means of real numbers are provided.