On Certain Properties for Two Classes of Generalized Convex Functions
Two classes of generalized convex functions in the sense of Beckenbach are considered. For both classes, we show that the existence of support curves implies their generalized convexity and obtain an extremum property of these functions. Furthermore, we establish Hadamard’s inequality for them.
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2016/4652038 |
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| _version_ | 1832562032627417088 |
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| author | Mohamed S. S. Ali |
| author_facet | Mohamed S. S. Ali |
| author_sort | Mohamed S. S. Ali |
| collection | DOAJ |
| description | Two classes of generalized convex functions in the sense of Beckenbach are considered. For both classes, we show that the existence of support curves implies their generalized convexity and obtain an extremum property of these functions. Furthermore, we establish Hadamard’s inequality for them. |
| format | Article |
| id | doaj-art-1624fa6de31f4e6d89b06d382b4ecd64 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1624fa6de31f4e6d89b06d382b4ecd642025-02-03T01:23:32ZengWileyAbstract and Applied Analysis1085-33751687-04092016-01-01201610.1155/2016/46520384652038On Certain Properties for Two Classes of Generalized Convex FunctionsMohamed S. S. Ali0Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, EgyptTwo classes of generalized convex functions in the sense of Beckenbach are considered. For both classes, we show that the existence of support curves implies their generalized convexity and obtain an extremum property of these functions. Furthermore, we establish Hadamard’s inequality for them.http://dx.doi.org/10.1155/2016/4652038 |
| spellingShingle | Mohamed S. S. Ali On Certain Properties for Two Classes of Generalized Convex Functions Abstract and Applied Analysis |
| title | On Certain Properties for Two Classes of Generalized Convex Functions |
| title_full | On Certain Properties for Two Classes of Generalized Convex Functions |
| title_fullStr | On Certain Properties for Two Classes of Generalized Convex Functions |
| title_full_unstemmed | On Certain Properties for Two Classes of Generalized Convex Functions |
| title_short | On Certain Properties for Two Classes of Generalized Convex Functions |
| title_sort | on certain properties for two classes of generalized convex functions |
| url | http://dx.doi.org/10.1155/2016/4652038 |
| work_keys_str_mv | AT mohamedssali oncertainpropertiesfortwoclassesofgeneralizedconvexfunctions |