On Extended Convex Functions via Incomplete Gamma Functions
Convex functions play an important role in many areas of mathematics. They are especially important in the study of optimization problems where they are distinguished by a number of convenient properties. In this paper, firstly we introduce the notion of h-exponential convex functions. This notion c...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/1924242 |
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| _version_ | 1850162424370429952 |
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| author | Yan Zhao M. Shoaib Saleem Shahid Mehmood Zabidin Salleh |
| author_facet | Yan Zhao M. Shoaib Saleem Shahid Mehmood Zabidin Salleh |
| author_sort | Yan Zhao |
| collection | DOAJ |
| description | Convex functions play an important role in many areas of mathematics. They are especially important in the study of optimization problems where they are distinguished by a number of convenient properties. In this paper, firstly we introduce the notion of h-exponential convex functions. This notion can be considered as generalizations of many existing definitions of convex functions. Then, we establish some well-known inequalities for the proposed notion via incomplete gamma functions. Precisely speaking, we established trapezoidal, midpoint, and He’s inequalities for h-exponential and harmonically exponential convex functions via incomplete gamma functions. Moreover, we gave several remarks to prove that our results are more generalized than the existing results in the literature. |
| format | Article |
| id | doaj-art-fe6e925fa5064907b616e5db02af948e |
| institution | OA Journals |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-fe6e925fa5064907b616e5db02af948e2025-08-20T02:22:34ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/19242421924242On Extended Convex Functions via Incomplete Gamma FunctionsYan Zhao0M. Shoaib Saleem1Shahid Mehmood2Zabidin Salleh3School of Medical Engineering, Xinxiang Medical University, Xinxiang, Henan 453003, ChinaDepartment of Mathematics, University of Okara, Okara, PakistanDepartment of Mathematics, University of Okara, Okara, PakistanDepartment of Mathematics, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, MalaysiaConvex functions play an important role in many areas of mathematics. They are especially important in the study of optimization problems where they are distinguished by a number of convenient properties. In this paper, firstly we introduce the notion of h-exponential convex functions. This notion can be considered as generalizations of many existing definitions of convex functions. Then, we establish some well-known inequalities for the proposed notion via incomplete gamma functions. Precisely speaking, we established trapezoidal, midpoint, and He’s inequalities for h-exponential and harmonically exponential convex functions via incomplete gamma functions. Moreover, we gave several remarks to prove that our results are more generalized than the existing results in the literature.http://dx.doi.org/10.1155/2021/1924242 |
| spellingShingle | Yan Zhao M. Shoaib Saleem Shahid Mehmood Zabidin Salleh On Extended Convex Functions via Incomplete Gamma Functions Journal of Function Spaces |
| title | On Extended Convex Functions via Incomplete Gamma Functions |
| title_full | On Extended Convex Functions via Incomplete Gamma Functions |
| title_fullStr | On Extended Convex Functions via Incomplete Gamma Functions |
| title_full_unstemmed | On Extended Convex Functions via Incomplete Gamma Functions |
| title_short | On Extended Convex Functions via Incomplete Gamma Functions |
| title_sort | on extended convex functions via incomplete gamma functions |
| url | http://dx.doi.org/10.1155/2021/1924242 |
| work_keys_str_mv | AT yanzhao onextendedconvexfunctionsviaincompletegammafunctions AT mshoaibsaleem onextendedconvexfunctionsviaincompletegammafunctions AT shahidmehmood onextendedconvexfunctionsviaincompletegammafunctions AT zabidinsalleh onextendedconvexfunctionsviaincompletegammafunctions |