New conticrete inequalities of the Hermite-Hadamard-Jensen-Mercer type in terms of generalized conformable fractional operators via majorization
The Hermite-Hadamard inequality is regarded as one of the most favorable inequalities from the research point of view. Currently, mathematicians are working on extending, improving, and generalizing this inequality. This article presents conticrete inequalities of the Hermite-Hadamard-Jensen-Mercer...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2023-05-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2022-0225 |
| _version_ | 1827938719186812928 |
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| author | Saeed Tareq Khan Muhammad Adil Faisal Shah Alsulami Hamed H. Alhodaly Mohammed Sh. |
| author_facet | Saeed Tareq Khan Muhammad Adil Faisal Shah Alsulami Hamed H. Alhodaly Mohammed Sh. |
| author_sort | Saeed Tareq |
| collection | DOAJ |
| description | The Hermite-Hadamard inequality is regarded as one of the most favorable inequalities from the research point of view. Currently, mathematicians are working on extending, improving, and generalizing this inequality. This article presents conticrete inequalities of the Hermite-Hadamard-Jensen-Mercer type in weighted and unweighted forms by using the idea of majorization and convexity together with generalized conformable fractional integral operators. They not only represent continuous and discrete inequalities in compact form but also produce generalized inequalities connecting various fractional operators such as Hadamard, Katugampola, Riemann-Liouville, conformable, and Rieman integrals into one single form. Also, two new integral identities have been investigated pertaining a differentiable function and three tuples. By using these identities and assuming ∣f′∣| f^{\prime} | and ∣f′∣q(q>1)| f^{\prime} {| }^{q}\hspace{0.33em}\left(q\gt 1) as convex, we deduce bounds concerning the discrepancy of the terms of the main inequalities. |
| first_indexed | 2024-03-13T08:42:04Z |
| format | Article |
| id | doaj.art-739999330ffd4fee952be0d4f00ce794 |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-03-13T08:42:04Z |
| publishDate | 2023-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-739999330ffd4fee952be0d4f00ce7942023-05-30T09:12:53ZengDe GruyterDemonstratio Mathematica2391-46612023-05-0156111210.1515/dema-2022-0225New conticrete inequalities of the Hermite-Hadamard-Jensen-Mercer type in terms of generalized conformable fractional operators via majorizationSaeed Tareq0Khan Muhammad Adil1Faisal Shah2Alsulami Hamed H.3Alhodaly Mohammed Sh.4Financial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, University of Peshawar, Peshawar 25000, PakistanDepartment of Mathematics, University of Peshawar, Peshawar 25000, PakistanFinancial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaFinancial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaThe Hermite-Hadamard inequality is regarded as one of the most favorable inequalities from the research point of view. Currently, mathematicians are working on extending, improving, and generalizing this inequality. This article presents conticrete inequalities of the Hermite-Hadamard-Jensen-Mercer type in weighted and unweighted forms by using the idea of majorization and convexity together with generalized conformable fractional integral operators. They not only represent continuous and discrete inequalities in compact form but also produce generalized inequalities connecting various fractional operators such as Hadamard, Katugampola, Riemann-Liouville, conformable, and Rieman integrals into one single form. Also, two new integral identities have been investigated pertaining a differentiable function and three tuples. By using these identities and assuming ∣f′∣| f^{\prime} | and ∣f′∣q(q>1)| f^{\prime} {| }^{q}\hspace{0.33em}\left(q\gt 1) as convex, we deduce bounds concerning the discrepancy of the terms of the main inequalities.https://doi.org/10.1515/dema-2022-0225jensen inequalitymercer inequalityhermite-hadamard inequalityhölder inequalitymajorization theory26d1526a5126a3326a42 |
| spellingShingle | Saeed Tareq Khan Muhammad Adil Faisal Shah Alsulami Hamed H. Alhodaly Mohammed Sh. New conticrete inequalities of the Hermite-Hadamard-Jensen-Mercer type in terms of generalized conformable fractional operators via majorization Demonstratio Mathematica jensen inequality mercer inequality hermite-hadamard inequality hölder inequality majorization theory 26d15 26a51 26a33 26a42 |
| title | New conticrete inequalities of the Hermite-Hadamard-Jensen-Mercer type in terms of generalized conformable fractional operators via majorization |
| title_full | New conticrete inequalities of the Hermite-Hadamard-Jensen-Mercer type in terms of generalized conformable fractional operators via majorization |
| title_fullStr | New conticrete inequalities of the Hermite-Hadamard-Jensen-Mercer type in terms of generalized conformable fractional operators via majorization |
| title_full_unstemmed | New conticrete inequalities of the Hermite-Hadamard-Jensen-Mercer type in terms of generalized conformable fractional operators via majorization |
| title_short | New conticrete inequalities of the Hermite-Hadamard-Jensen-Mercer type in terms of generalized conformable fractional operators via majorization |
| title_sort | new conticrete inequalities of the hermite hadamard jensen mercer type in terms of generalized conformable fractional operators via majorization |
| topic | jensen inequality mercer inequality hermite-hadamard inequality hölder inequality majorization theory 26d15 26a51 26a33 26a42 |
| url | https://doi.org/10.1515/dema-2022-0225 |
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