Properties and Bounds of Jensen-Type Functionals via Harmonic Convex Functions
Dragomir introduced the Jensen-type inequality for harmonic convex functions (HCF) and Baloch et al. studied its different variants, such as Jensen-type inequality for harmonic h-convex functions. In this paper, we aim to establish the functional form of inequalities presented by Baloch et al. and p...
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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 Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5561611 |
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| _version_ | 1832545914340769792 |
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| author | Aqeel Ahmad Mughal Hassan Almusawa Absar Ul Haq Imran Abbas Baloch |
| author_facet | Aqeel Ahmad Mughal Hassan Almusawa Absar Ul Haq Imran Abbas Baloch |
| author_sort | Aqeel Ahmad Mughal |
| collection | DOAJ |
| description | Dragomir introduced the Jensen-type inequality for harmonic convex functions (HCF) and Baloch et al. studied its different variants, such as Jensen-type inequality for harmonic h-convex functions. In this paper, we aim to establish the functional form of inequalities presented by Baloch et al. and prove the superadditivity and monotonicity properties of these functionals. Furthermore, we derive the bound for these functionals under certain conditions. Furthermore, we define more generalized functionals involving monotonic nondecreasing concave function as well as evince superadditivity and monotonicity properties of these generalized functionals. |
| format | Article |
| id | doaj-art-41c6a77e6a44412e81c9ffdf386c0b40 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-41c6a77e6a44412e81c9ffdf386c0b402025-02-03T07:24:24ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55616115561611Properties and Bounds of Jensen-Type Functionals via Harmonic Convex FunctionsAqeel Ahmad Mughal0Hassan Almusawa1Absar Ul Haq2Imran Abbas Baloch3Department of Mathematics and Statistics, University of Lahore, Lahore, PakistanDepartment of Mathematics, College of Sciences, Jazan University, Jazan 45142, Saudi ArabiaDepartment of Natural Sciences and Humanities, University of Engineering and Technology (Narowal Campus), Lahore 54000, PakistanAbdus Salam School of Mathematical Sciences, GC University, Lahore, PakistanDragomir introduced the Jensen-type inequality for harmonic convex functions (HCF) and Baloch et al. studied its different variants, such as Jensen-type inequality for harmonic h-convex functions. In this paper, we aim to establish the functional form of inequalities presented by Baloch et al. and prove the superadditivity and monotonicity properties of these functionals. Furthermore, we derive the bound for these functionals under certain conditions. Furthermore, we define more generalized functionals involving monotonic nondecreasing concave function as well as evince superadditivity and monotonicity properties of these generalized functionals.http://dx.doi.org/10.1155/2021/5561611 |
| spellingShingle | Aqeel Ahmad Mughal Hassan Almusawa Absar Ul Haq Imran Abbas Baloch Properties and Bounds of Jensen-Type Functionals via Harmonic Convex Functions Journal of Mathematics |
| title | Properties and Bounds of Jensen-Type Functionals via Harmonic Convex Functions |
| title_full | Properties and Bounds of Jensen-Type Functionals via Harmonic Convex Functions |
| title_fullStr | Properties and Bounds of Jensen-Type Functionals via Harmonic Convex Functions |
| title_full_unstemmed | Properties and Bounds of Jensen-Type Functionals via Harmonic Convex Functions |
| title_short | Properties and Bounds of Jensen-Type Functionals via Harmonic Convex Functions |
| title_sort | properties and bounds of jensen type functionals via harmonic convex functions |
| url | http://dx.doi.org/10.1155/2021/5561611 |
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