Some Generalizations of Integral Inequalities and Their Applications

TL;DR

This paper generalizes an integral identity for twice differentiable functions, deriving new inequalities using convexity and classical inequalities, with applications to quadrature formulas and means.

Contribution

It introduces a generalized integral identity and new inequalities based on convexity, extending previous results and providing practical applications.

Findings

New integral inequalities for twice differentiable functions

Applications to quadrature formulas and special means

Extension of previous results by specific parameter choices

Abstract

In this paper, an integral identity for twice differentiable functions is generalized. Then, by using convexity of |f''| or q-th power of |f''| and with the aid of power mean and Holder's inequalities we achieved some new results. We also gave some applications to quadrature formulas and some special means. Therewithal, by choosing (alpha=1/2) in our main results, we obtained some findings in [13].