$k$-fractional integral inequalities of Hadamard type for exponentially $(s,m)$-convex functions
The aim of this article is to present fractional versions of the Hadamard type inequalities for exponentially $(s, m)$-convex functions via $k$-analogue of Riemann-Liouville fractional integrals. The results provide generalizations of various known fractional integral inequalities. Some special case...
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2021052/fulltext.html |
| _version_ | 1818189140977516544 |
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| author | Atiq Ur Rehman Ghulam Farid Sidra Bibi Chahn Yong Jung Shin Min Kang |
| author_facet | Atiq Ur Rehman Ghulam Farid Sidra Bibi Chahn Yong Jung Shin Min Kang |
| author_sort | Atiq Ur Rehman |
| collection | DOAJ |
| description | The aim of this article is to present fractional versions of the Hadamard type inequalities for exponentially $(s, m)$-convex functions via $k$-analogue of Riemann-Liouville fractional integrals. The results provide generalizations of various known fractional integral inequalities. Some special cases are analyzed in the form of corollaries and remarks. |
| first_indexed | 2024-12-11T23:38:06Z |
| format | Article |
| id | doaj.art-dad6efb5815144df81386c12cdd85116 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-11T23:38:06Z |
| publishDate | 2021-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-dad6efb5815144df81386c12cdd851162022-12-22T00:45:48ZengAIMS PressAIMS Mathematics2473-69882021-11-016188289210.3934/math.2021052$k$-fractional integral inequalities of Hadamard type for exponentially $(s,m)$-convex functionsAtiq Ur Rehman0Ghulam Farid1Sidra Bibi2Chahn Yong Jung3Shin Min Kang41 COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan1 COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan2 Govt. Girls Primary School Kamra Khurd, Attock 43570, Pakistan3 Department of Business Administration, Gyeongsang National University Jinju 52828, Korea4 Center for General Education, China Medical University, Taichung 40402, TaiwanThe aim of this article is to present fractional versions of the Hadamard type inequalities for exponentially $(s, m)$-convex functions via $k$-analogue of Riemann-Liouville fractional integrals. The results provide generalizations of various known fractional integral inequalities. Some special cases are analyzed in the form of corollaries and remarks.https://www.aimspress.com/article/10.3934/math.2021052/fulltext.htmlconvex functionshadamard inequalityriemann-liouville fractional integral operators |
| spellingShingle | Atiq Ur Rehman Ghulam Farid Sidra Bibi Chahn Yong Jung Shin Min Kang $k$-fractional integral inequalities of Hadamard type for exponentially $(s,m)$-convex functions AIMS Mathematics convex functions hadamard inequality riemann-liouville fractional integral operators |
| title | $k$-fractional integral inequalities of Hadamard type for exponentially $(s,m)$-convex functions |
| title_full | $k$-fractional integral inequalities of Hadamard type for exponentially $(s,m)$-convex functions |
| title_fullStr | $k$-fractional integral inequalities of Hadamard type for exponentially $(s,m)$-convex functions |
| title_full_unstemmed | $k$-fractional integral inequalities of Hadamard type for exponentially $(s,m)$-convex functions |
| title_short | $k$-fractional integral inequalities of Hadamard type for exponentially $(s,m)$-convex functions |
| title_sort | k fractional integral inequalities of hadamard type for exponentially s m convex functions |
| topic | convex functions hadamard inequality riemann-liouville fractional integral operators |
| url | https://www.aimspress.com/article/10.3934/math.2021052/fulltext.html |
| work_keys_str_mv | AT atiqurrehman kfractionalintegralinequalitiesofhadamardtypeforexponentiallysmconvexfunctions AT ghulamfarid kfractionalintegralinequalitiesofhadamardtypeforexponentiallysmconvexfunctions AT sidrabibi kfractionalintegralinequalitiesofhadamardtypeforexponentiallysmconvexfunctions AT chahnyongjung kfractionalintegralinequalitiesofhadamardtypeforexponentiallysmconvexfunctions AT shinminkang kfractionalintegralinequalitiesofhadamardtypeforexponentiallysmconvexfunctions |