Cauchy type means for some generalized convex functions
Abstract In this paper, we establish Jensen’s inequality for s-convex functions in the first sense. By using Jensen’s inequalities, we obtain some Cauchy type means for p-convex and s-convex functions in the first sense. Also, by using Hermite–Hadamard inequalities for the respective generalized con...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-07-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-021-02647-2 |
| _version_ | 1818907597843988480 |
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| author | Naila Mehreen Matloob Anwar |
| author_facet | Naila Mehreen Matloob Anwar |
| author_sort | Naila Mehreen |
| collection | DOAJ |
| description | Abstract In this paper, we establish Jensen’s inequality for s-convex functions in the first sense. By using Jensen’s inequalities, we obtain some Cauchy type means for p-convex and s-convex functions in the first sense. Also, by using Hermite–Hadamard inequalities for the respective generalized convex functions, we find new generalized Cauchy type means. |
| first_indexed | 2024-12-19T21:57:39Z |
| format | Article |
| id | doaj.art-3403b9c0d17144c29406f57b1d8bfcb1 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-19T21:57:39Z |
| publishDate | 2021-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-3403b9c0d17144c29406f57b1d8bfcb12022-12-21T20:04:15ZengSpringerOpenJournal of Inequalities and Applications1029-242X2021-07-012021111310.1186/s13660-021-02647-2Cauchy type means for some generalized convex functionsNaila Mehreen0Matloob Anwar1School of Natural Sciences, National University of Sciences and TechnologySchool of Natural Sciences, National University of Sciences and TechnologyAbstract In this paper, we establish Jensen’s inequality for s-convex functions in the first sense. By using Jensen’s inequalities, we obtain some Cauchy type means for p-convex and s-convex functions in the first sense. Also, by using Hermite–Hadamard inequalities for the respective generalized convex functions, we find new generalized Cauchy type means.https://doi.org/10.1186/s13660-021-02647-2Cauchy mean value theoremJensen’s inequalityHermite–Hadamard inequalityp-convex functions-convex function in the first sense |
| spellingShingle | Naila Mehreen Matloob Anwar Cauchy type means for some generalized convex functions Journal of Inequalities and Applications Cauchy mean value theorem Jensen’s inequality Hermite–Hadamard inequality p-convex function s-convex function in the first sense |
| title | Cauchy type means for some generalized convex functions |
| title_full | Cauchy type means for some generalized convex functions |
| title_fullStr | Cauchy type means for some generalized convex functions |
| title_full_unstemmed | Cauchy type means for some generalized convex functions |
| title_short | Cauchy type means for some generalized convex functions |
| title_sort | cauchy type means for some generalized convex functions |
| topic | Cauchy mean value theorem Jensen’s inequality Hermite–Hadamard inequality p-convex function s-convex function in the first sense |
| url | https://doi.org/10.1186/s13660-021-02647-2 |
| work_keys_str_mv | AT nailamehreen cauchytypemeansforsomegeneralizedconvexfunctions AT matloobanwar cauchytypemeansforsomegeneralizedconvexfunctions |