Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex Functions
In this paper, we define a new function, namely, harmonically α,h−m-convex function, which unifies various kinds of harmonically convex functions. Generalized versions of the Hadamard and the Fejér–Hadamard fractional integral inequalities for harmonically α,h−m-convex functions via generalized frac...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/8245324 |
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| _version_ | 1832551686342705152 |
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| author | Chahn Yong Jung Muhammad Yussouf Yu-Ming Chu Ghulam Farid Shin Min Kang |
| author_facet | Chahn Yong Jung Muhammad Yussouf Yu-Ming Chu Ghulam Farid Shin Min Kang |
| author_sort | Chahn Yong Jung |
| collection | DOAJ |
| description | In this paper, we define a new function, namely, harmonically α,h−m-convex function, which unifies various kinds of harmonically convex functions. Generalized versions of the Hadamard and the Fejér–Hadamard fractional integral inequalities for harmonically α,h−m-convex functions via generalized fractional integral operators are proved. From presented results, a series of fractional integral inequalities can be obtained for harmonically convex, harmonically h−m-convex, harmonically α,m-convex, and related functions and for already known fractional integral operators. |
| format | Article |
| id | doaj-art-8ce0c6a91e8849f4933808c7b1073b43 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-8ce0c6a91e8849f4933808c7b1073b432025-02-03T06:00:49ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/82453248245324Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex FunctionsChahn Yong Jung0Muhammad Yussouf1Yu-Ming Chu2Ghulam Farid3Shin Min Kang4Department of Business Administration, Gyeongsang National University, Jinju 52828, Republic of KoreaDepartment of Mathematics, University of Sargodha, Sargodha, PakistanDepartment of Mathematics, Huzhou University, Huzhou 313000, ChinaDepartment of Mathematics, COMSATS University Islamabad, Attock, PakistanCenter for General Education, China Medical University, Taichung 40402, TaiwanIn this paper, we define a new function, namely, harmonically α,h−m-convex function, which unifies various kinds of harmonically convex functions. Generalized versions of the Hadamard and the Fejér–Hadamard fractional integral inequalities for harmonically α,h−m-convex functions via generalized fractional integral operators are proved. From presented results, a series of fractional integral inequalities can be obtained for harmonically convex, harmonically h−m-convex, harmonically α,m-convex, and related functions and for already known fractional integral operators.http://dx.doi.org/10.1155/2020/8245324 |
| spellingShingle | Chahn Yong Jung Muhammad Yussouf Yu-Ming Chu Ghulam Farid Shin Min Kang Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex Functions Journal of Mathematics |
| title | Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex Functions |
| title_full | Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex Functions |
| title_fullStr | Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex Functions |
| title_full_unstemmed | Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex Functions |
| title_short | Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex Functions |
| title_sort | generalized fractional hadamard and fejer hadamard inequalities for generalized harmonically convex functions |
| url | http://dx.doi.org/10.1155/2020/8245324 |
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