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通过分数阶积分算子的布伦型不等式的进展及其应用

Advancements in Bullen-type inequalities via fractional integral operators and their applications.

作者信息

Samraiz Muhammad, Hassan Zohaib, Naheed Saima, Vivas-Cortez Miguel, Ali Rifaqat, Lamoudan Tarik

机构信息

Department of Mathematics, University of Sargodha, P.O. Box 40100, Sargodha, Pakistan.

Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Católica del Ecuador, Av. 12 de octubre 1076, Apartado, Quito 17-01-2184, Ecuador.

出版信息

Heliyon. 2024 Sep 3;10(17):e37246. doi: 10.1016/j.heliyon.2024.e37246. eCollection 2024 Sep 15.

Abstract

In this paper, we investigate Bullen-type inequalities applicable to functions that are twice-differentiable. To explore these advanced inequalities, we utilize generalized convexity and Riemann-type fractional integrals. A comparative analysis is provided to highlight the more refined inequalities from among the explored results. By exploring the limiting cases, a relation with existing literature is established. Several examples are also presented to illustrate the outcomes and their accuracy is validated through graphical analysis. Additionally, applications in generalized means are also discussed.

摘要

在本文中,我们研究适用于二次可微函数的布伦型不等式。为了探究这些高级不等式,我们利用广义凸性和黎曼型分数积分。提供了一个比较分析,以突出所探究结果中更精确的不等式。通过探究极限情况,建立了与现有文献的关系。还给出了几个例子来说明结果,并通过图形分析验证了它们的准确性。此外,还讨论了在广义均值中的应用。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8883/11408068/bd01c5a804df/gr001.jpg

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