积分不等式的一些新估计及其应用

Pub Date : 2024-08-16 DOI:10.1007/s11253-024-02315-w

B. Bayraktar, S. I. Butt, J. E. Nápoles, F. Rabossi

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引用次数: 0

摘要

对于一阶导数满足拉格朗日定理条件或李普希兹条件的函数，我们用分数积分算子得到了几个新的积分不等式。在某些特殊情况下，与文献中已知的布伦型不等式和哈达玛型右侧不等式的结果相比，所获得的结果提供了更好的上估计值。最后，讨论了梯形公式的一些误差估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Some New Estimates for Integral Inequalities and Their Applications

We obtain several new integral inequalities in terms of fractional integral operators for the functions whose first derivatives satisfy either the conditions of the Lagrange theorem or the Lipschitz condition. In some special cases, the obtained results provide better upper estimates than the results known in the literature for the Bullen-type inequality and the Hadamard-type right-hand side inequality. Finally, some error estimates for the trapezoidal formula are discussed.

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