A novel fractional approach to finding the upper bounds of Simpson and Hermite-Hadamard-type inequalities in tensorial Hilbert spaces by using differentiable convex mappings
Function spaces are significant in the study and application of mathematical inequalities. The objective of this article is to develop several new bounds and refinements for well-known inequalities that involve Hilbert spaces within a tensorial framework. Using self-adjoint operators in tensor Hilbe...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-12-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241671 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590742705405952 |
|---|---|
| author | Zareen A. Khan Waqar Afzal Mujahid Abbas Jongsuk Ro Najla M. Aloraini |
| author_facet | Zareen A. Khan Waqar Afzal Mujahid Abbas Jongsuk Ro Najla M. Aloraini |
| author_sort | Zareen A. Khan |
| collection | DOAJ |
| description | Function spaces are significant in the study and application of mathematical inequalities. The objective of this article is to develop several new bounds and refinements for well-known inequalities that involve Hilbert spaces within a tensorial framework. Using self-adjoint operators in tensor Hilbert spaces, we developed Simpson type inequalities by using different types of generalized convex mappings. Our next step involved developing a variety of new variations of the Hermite and Hadamard inequalities using convex mappings with some special means, specifically arithmetic and geometric means. Furthermore, we developed a number of new fractional identities, which are used in our main findings, by using Riemann-Liouville integrals. In addition, we discuss some examples involving log convex functions and their consequences. |
| format | Article |
| id | doaj-art-4ea122ec342e4b5191191949e82f11ee |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-4ea122ec342e4b5191191949e82f11ee2025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912351513518010.3934/math.20241671A novel fractional approach to finding the upper bounds of Simpson and Hermite-Hadamard-type inequalities in tensorial Hilbert spaces by using differentiable convex mappingsZareen A. Khan0Waqar Afzal1Mujahid Abbas2Jongsuk Ro3Najla M. Aloraini4Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Mathematics, Government College University, Katchery Road, Lahore 54000, PakistanDepartment of Mechanical Engineering Sciences, Faculty of Engineering and the Built Environment, Doornfontein Campus, University of Johannesburg, South AfricaSchool of Electrical and Electronics Engineering, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of KoreaDepartment of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi ArabiaFunction spaces are significant in the study and application of mathematical inequalities. The objective of this article is to develop several new bounds and refinements for well-known inequalities that involve Hilbert spaces within a tensorial framework. Using self-adjoint operators in tensor Hilbert spaces, we developed Simpson type inequalities by using different types of generalized convex mappings. Our next step involved developing a variety of new variations of the Hermite and Hadamard inequalities using convex mappings with some special means, specifically arithmetic and geometric means. Furthermore, we developed a number of new fractional identities, which are used in our main findings, by using Riemann-Liouville integrals. In addition, we discuss some examples involving log convex functions and their consequences.https://www.aimspress.com/article/doi/10.3934/math.20241671hermite-hadamardfractional calculusupper boundsmathematical operators |
| spellingShingle | Zareen A. Khan Waqar Afzal Mujahid Abbas Jongsuk Ro Najla M. Aloraini A novel fractional approach to finding the upper bounds of Simpson and Hermite-Hadamard-type inequalities in tensorial Hilbert spaces by using differentiable convex mappings AIMS Mathematics hermite-hadamard fractional calculus upper bounds mathematical operators |
| title | A novel fractional approach to finding the upper bounds of Simpson and Hermite-Hadamard-type inequalities in tensorial Hilbert spaces by using differentiable convex mappings |
| title_full | A novel fractional approach to finding the upper bounds of Simpson and Hermite-Hadamard-type inequalities in tensorial Hilbert spaces by using differentiable convex mappings |
| title_fullStr | A novel fractional approach to finding the upper bounds of Simpson and Hermite-Hadamard-type inequalities in tensorial Hilbert spaces by using differentiable convex mappings |
| title_full_unstemmed | A novel fractional approach to finding the upper bounds of Simpson and Hermite-Hadamard-type inequalities in tensorial Hilbert spaces by using differentiable convex mappings |
| title_short | A novel fractional approach to finding the upper bounds of Simpson and Hermite-Hadamard-type inequalities in tensorial Hilbert spaces by using differentiable convex mappings |
| title_sort | novel fractional approach to finding the upper bounds of simpson and hermite hadamard type inequalities in tensorial hilbert spaces by using differentiable convex mappings |
| topic | hermite-hadamard fractional calculus upper bounds mathematical operators |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241671 |
| work_keys_str_mv | AT zareenakhan anovelfractionalapproachtofindingtheupperboundsofsimpsonandhermitehadamardtypeinequalitiesintensorialhilbertspacesbyusingdifferentiableconvexmappings AT waqarafzal anovelfractionalapproachtofindingtheupperboundsofsimpsonandhermitehadamardtypeinequalitiesintensorialhilbertspacesbyusingdifferentiableconvexmappings AT mujahidabbas anovelfractionalapproachtofindingtheupperboundsofsimpsonandhermitehadamardtypeinequalitiesintensorialhilbertspacesbyusingdifferentiableconvexmappings AT jongsukro anovelfractionalapproachtofindingtheupperboundsofsimpsonandhermitehadamardtypeinequalitiesintensorialhilbertspacesbyusingdifferentiableconvexmappings AT najlamaloraini anovelfractionalapproachtofindingtheupperboundsofsimpsonandhermitehadamardtypeinequalitiesintensorialhilbertspacesbyusingdifferentiableconvexmappings AT zareenakhan novelfractionalapproachtofindingtheupperboundsofsimpsonandhermitehadamardtypeinequalitiesintensorialhilbertspacesbyusingdifferentiableconvexmappings AT waqarafzal novelfractionalapproachtofindingtheupperboundsofsimpsonandhermitehadamardtypeinequalitiesintensorialhilbertspacesbyusingdifferentiableconvexmappings AT mujahidabbas novelfractionalapproachtofindingtheupperboundsofsimpsonandhermitehadamardtypeinequalitiesintensorialhilbertspacesbyusingdifferentiableconvexmappings AT jongsukro novelfractionalapproachtofindingtheupperboundsofsimpsonandhermitehadamardtypeinequalitiesintensorialhilbertspacesbyusingdifferentiableconvexmappings AT najlamaloraini novelfractionalapproachtofindingtheupperboundsofsimpsonandhermitehadamardtypeinequalitiesintensorialhilbertspacesbyusingdifferentiableconvexmappings |