Fractional Ostrowski Type Inequalities via $\phi-\lambda-$Convex Function
In this paper, we aim to state well-known Ostrowski inequality via fractional Montgomery identity for the class of $\phi-\lambda-$ convex functions. This generalized class of convex function contains other well-known convex functions from literature, allowing us to derive Ostrowski-type inequalitie...
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| Format: | Article |
| Language: | English |
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University of Maragheh
2024-01-01
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| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | https://scma.maragheh.ac.ir/article_707159_e4569d0e700493a24df2253d4946b387.pdf |
| _version_ | 1797359784248213504 |
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| author | Ali Hassan Asif Khan |
| author_facet | Ali Hassan Asif Khan |
| author_sort | Ali Hassan |
| collection | DOAJ |
| description | In this paper, we aim to state well-known Ostrowski inequality via fractional Montgomery identity for the class of $\phi-\lambda-$ convex functions. This generalized class of convex function contains other well-known convex functions from literature, allowing us to derive Ostrowski-type inequalities as specific instances. Moreover, we present Ostrowski-type inequalities for which certain powers of absolute derivatives are $\phi-\lambda-$ convex using various techniques, including Hölder's inequality and the power mean inequality. Consequently, various established results would be captured as special cases. Moreover, we provide applications in terms of special means, allowing us to derive many numerical inequalities related to special means from Ostrowski-type inequalities. |
| first_indexed | 2024-03-08T15:29:47Z |
| format | Article |
| id | doaj.art-b14fc83deacf4c4fab18ee9a19e15982 |
| institution | Directory Open Access Journal |
| issn | 2322-5807 2423-3900 |
| language | English |
| last_indexed | 2024-03-08T15:29:47Z |
| publishDate | 2024-01-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj.art-b14fc83deacf4c4fab18ee9a19e159822024-01-10T07:27:09ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002024-01-0121111112910.22130/scma.2022.537502.976707159Fractional Ostrowski Type Inequalities via $\phi-\lambda-$Convex FunctionAli Hassan0Asif Khan1Department of Mathematics, Shah Abdul Latif University Khairpur-66020, Pakistan.Department of Mathematics, University of Karachi, University Road, Karachi-75270, Pakistan.In this paper, we aim to state well-known Ostrowski inequality via fractional Montgomery identity for the class of $\phi-\lambda-$ convex functions. This generalized class of convex function contains other well-known convex functions from literature, allowing us to derive Ostrowski-type inequalities as specific instances. Moreover, we present Ostrowski-type inequalities for which certain powers of absolute derivatives are $\phi-\lambda-$ convex using various techniques, including Hölder's inequality and the power mean inequality. Consequently, various established results would be captured as special cases. Moreover, we provide applications in terms of special means, allowing us to derive many numerical inequalities related to special means from Ostrowski-type inequalities.https://scma.maragheh.ac.ir/article_707159_e4569d0e700493a24df2253d4946b387.pdfostrowski inequalityconvexpower mean inequalityhölder's inequality |
| spellingShingle | Ali Hassan Asif Khan Fractional Ostrowski Type Inequalities via $\phi-\lambda-$Convex Function Sahand Communications in Mathematical Analysis ostrowski inequality convex power mean inequality hölder's inequality |
| title | Fractional Ostrowski Type Inequalities via $\phi-\lambda-$Convex Function |
| title_full | Fractional Ostrowski Type Inequalities via $\phi-\lambda-$Convex Function |
| title_fullStr | Fractional Ostrowski Type Inequalities via $\phi-\lambda-$Convex Function |
| title_full_unstemmed | Fractional Ostrowski Type Inequalities via $\phi-\lambda-$Convex Function |
| title_short | Fractional Ostrowski Type Inequalities via $\phi-\lambda-$Convex Function |
| title_sort | fractional ostrowski type inequalities via phi lambda convex function |
| topic | ostrowski inequality convex power mean inequality hölder's inequality |
| url | https://scma.maragheh.ac.ir/article_707159_e4569d0e700493a24df2253d4946b387.pdf |
| work_keys_str_mv | AT alihassan fractionalostrowskitypeinequalitiesviaphilambdaconvexfunction AT asifkhan fractionalostrowskitypeinequalitiesviaphilambdaconvexfunction |