Hermite-Jensen-Mercer type inequalities via Ψ-Riemann-Liouville <em>k</em>-fractional integrals
Integral inequalities involving various fractional integral operators are used to solve many fractional differential equations. In this paper, authors prove some Hermite-Jensen-Mercer type inequalities using Ψ-Riemann-Liouville <em>k</em>-Fractional integrals via convex functions. We est...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-07-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2020334/fulltext.html |
| _version_ | 1818435881373007872 |
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| author | Saad Ihsan Butt Artion Kashuri Muhammad Umar Adnan Aslam Wei Gao |
| author_facet | Saad Ihsan Butt Artion Kashuri Muhammad Umar Adnan Aslam Wei Gao |
| author_sort | Saad Ihsan Butt |
| collection | DOAJ |
| description | Integral inequalities involving various fractional integral operators are used to solve many fractional differential equations. In this paper, authors prove some Hermite-Jensen-Mercer type inequalities using Ψ-Riemann-Liouville <em>k</em>-Fractional integrals via convex functions. We established some new Ψ-Riemann-Liouville <em>k</em>-Fractional integral inequalities. We also give Ψ-Riemann-Liouville <em>k</em>-Fractional integrals identities for differentiable mapping, and these will be used to derive estimates for some fractional Hermite-Jensen-Mercer type inequalities. Some known results are recaptured from our results as special cases. |
| first_indexed | 2024-12-14T16:59:56Z |
| format | Article |
| id | doaj.art-873a3a873b264f4286ee0e604bbd135c |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-14T16:59:56Z |
| publishDate | 2020-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-873a3a873b264f4286ee0e604bbd135c2022-12-21T22:53:52ZengAIMS PressAIMS Mathematics2473-69882020-07-01555193522010.3934/math.2020334Hermite-Jensen-Mercer type inequalities via Ψ-Riemann-Liouville <em>k</em>-fractional integralsSaad Ihsan Butt0Artion Kashuri1Muhammad Umar2Adnan Aslam3Wei Gao41 Department of Mathematics, COMSATS University Islamabad, Lahore Campus 54000, Pakistan2 Department of Mathematics, Faculty of Technical Science, University “Ismail Qemali”, Vlora, Albania1 Department of Mathematics, COMSATS University Islamabad, Lahore Campus 54000, Pakistan3 Department of Natural Sciences and Humanities, University of Engineering and Technology, Lahore(RCET) 54000, Pakistan4 School of Information Science and Technology, Yunnan Normal University, Kunming 650500, ChinaIntegral inequalities involving various fractional integral operators are used to solve many fractional differential equations. In this paper, authors prove some Hermite-Jensen-Mercer type inequalities using Ψ-Riemann-Liouville <em>k</em>-Fractional integrals via convex functions. We established some new Ψ-Riemann-Liouville <em>k</em>-Fractional integral inequalities. We also give Ψ-Riemann-Liouville <em>k</em>-Fractional integrals identities for differentiable mapping, and these will be used to derive estimates for some fractional Hermite-Jensen-Mercer type inequalities. Some known results are recaptured from our results as special cases.https://www.aimspress.com/article/10.3934/math.2020334/fulltext.htmlconvex functionhermite-hadamard inequalityjensen inequalityjensen-mercer inequalityhölder inequalityimproved power mean integral inequality<i>ψ</i>-riemann-liouville <i>k</i>-fractional integrals |
| spellingShingle | Saad Ihsan Butt Artion Kashuri Muhammad Umar Adnan Aslam Wei Gao Hermite-Jensen-Mercer type inequalities via Ψ-Riemann-Liouville <em>k</em>-fractional integrals AIMS Mathematics convex function hermite-hadamard inequality jensen inequality jensen-mercer inequality hölder inequality improved power mean integral inequality <i>ψ</i>-riemann-liouville <i>k</i>-fractional integrals |
| title | Hermite-Jensen-Mercer type inequalities via Ψ-Riemann-Liouville <em>k</em>-fractional integrals |
| title_full | Hermite-Jensen-Mercer type inequalities via Ψ-Riemann-Liouville <em>k</em>-fractional integrals |
| title_fullStr | Hermite-Jensen-Mercer type inequalities via Ψ-Riemann-Liouville <em>k</em>-fractional integrals |
| title_full_unstemmed | Hermite-Jensen-Mercer type inequalities via Ψ-Riemann-Liouville <em>k</em>-fractional integrals |
| title_short | Hermite-Jensen-Mercer type inequalities via Ψ-Riemann-Liouville <em>k</em>-fractional integrals |
| title_sort | hermite jensen mercer type inequalities via ψ riemann liouville em k em fractional integrals |
| topic | convex function hermite-hadamard inequality jensen inequality jensen-mercer inequality hölder inequality improved power mean integral inequality <i>ψ</i>-riemann-liouville <i>k</i>-fractional integrals |
| url | https://www.aimspress.com/article/10.3934/math.2020334/fulltext.html |
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