AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home AIMS Mathematics Article
PDF (462.1 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

Milne-Type inequalities via expanded fractional operators: A comparative study with different types of functions

Abd-Allah Hyder1( ), Hüseyin Budak2, Mohamed A. Barakat3,4
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Türkiye
Department of Computer Science, College of Al Wajh, University of Tabuk, Saudi Arabia
Department of Mathematics, Faculty of Sciences, Al-Azhar University, Assiut 71524, Egypt
Show Author Information

Abstract

This study focused on deriving Milne-type inequalities using expanded fractional integral operators. We began by establishing a key equality associated with these operators. Using this equality, we explored Milne-type inequalities for functions with convex derivatives, supported by an illustrative example for clarity. Additionally, we investigated Milne-type inequalities for bounded and Lipschitzian functions utilizing fractional expanded integrals. Finally, we extended our exploration to Milne-type inequalities involving functions of bounded variation.

Keywords

fractional integralsMilne-type inequalitiesfunctions of bounded variationconvex functionsbounded functions
CLC number: 26D15, 26D10, 26D07

References

【1】
【1】
 
 
Crossref Google Scholar
AIMS Mathematics
Volume 9 Issue 5,
May 2024
Pages 11228-11246
DOI: 10.3934/math.2024551

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
Hyder A-A, Budak H, Barakat MA. Milne-Type inequalities via expanded fractional operators: A comparative study with different types of functions. AIMS Mathematics, 2024, 9(5): 11228-11246. https://doi.org/10.3934/math.2024551

5

Views

0

Downloads

0

Crossref

0

Web of Science

5

Scopus
Received: 25 December 2023
Revised: 10 February 2024
Accepted: 19 February 2024
Published: 15 May 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)