Jensen–Mercer inequality for GA-convex functions and some related inequalities
Abstract In this paper, firstly, we prove a Jensen–Mercer inequality for GA-convex functions. After that, we establish weighted Hermite–Hadamard’s inequalities for GA-convex functions using the new Jensen–Mercer inequality, and we establish some new inequalities connected with Hermite–Hadamard–Merce...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-08-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | http://link.springer.com/article/10.1186/s13660-020-02478-7 |
| _version_ | 1818213769117958144 |
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| author | İmdat İşcan |
| author_facet | İmdat İşcan |
| author_sort | İmdat İşcan |
| collection | DOAJ |
| description | Abstract In this paper, firstly, we prove a Jensen–Mercer inequality for GA-convex functions. After that, we establish weighted Hermite–Hadamard’s inequalities for GA-convex functions using the new Jensen–Mercer inequality, and we establish some new inequalities connected with Hermite–Hadamard–Mercer type inequalities for differentiable mappings whose derivatives in absolute value are GA-convex. |
| first_indexed | 2024-12-12T06:09:33Z |
| format | Article |
| id | doaj.art-a5a4124decbc4cb3a7323bed814edfff |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-12T06:09:33Z |
| publishDate | 2020-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-a5a4124decbc4cb3a7323bed814edfff2022-12-22T00:35:11ZengSpringerOpenJournal of Inequalities and Applications1029-242X2020-08-012020111610.1186/s13660-020-02478-7Jensen–Mercer inequality for GA-convex functions and some related inequalitiesİmdat İşcan0Department of Mathematics, Faculty of Arts and Sciences, Giresun UniversityAbstract In this paper, firstly, we prove a Jensen–Mercer inequality for GA-convex functions. After that, we establish weighted Hermite–Hadamard’s inequalities for GA-convex functions using the new Jensen–Mercer inequality, and we establish some new inequalities connected with Hermite–Hadamard–Mercer type inequalities for differentiable mappings whose derivatives in absolute value are GA-convex.http://link.springer.com/article/10.1186/s13660-020-02478-7GA-convex functionJensen–Mercer inequalityHadamard fractional integralsHermite–Hadamard inequality |
| spellingShingle | İmdat İşcan Jensen–Mercer inequality for GA-convex functions and some related inequalities Journal of Inequalities and Applications GA-convex function Jensen–Mercer inequality Hadamard fractional integrals Hermite–Hadamard inequality |
| title | Jensen–Mercer inequality for GA-convex functions and some related inequalities |
| title_full | Jensen–Mercer inequality for GA-convex functions and some related inequalities |
| title_fullStr | Jensen–Mercer inequality for GA-convex functions and some related inequalities |
| title_full_unstemmed | Jensen–Mercer inequality for GA-convex functions and some related inequalities |
| title_short | Jensen–Mercer inequality for GA-convex functions and some related inequalities |
| title_sort | jensen mercer inequality for ga convex functions and some related inequalities |
| topic | GA-convex function Jensen–Mercer inequality Hadamard fractional integrals Hermite–Hadamard inequality |
| url | http://link.springer.com/article/10.1186/s13660-020-02478-7 |
| work_keys_str_mv | AT imdatiscan jensenmercerinequalityforgaconvexfunctionsandsomerelatedinequalities |