On Semi-(B,G)-Preinvex Functions
We firstly construct a concrete semi-invex set which is not invex. Basing on concept of semi-invex set, we introduce some kinds of generalized convex functions, which include semi-(B,G)-preinvex functions, strictly semi-(B,G)-preinvex functions and explicitly semi-(B,G)-preinvex functions. Moreover,...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/530468 |
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| _version_ | 1850106796932333568 |
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| author | Xiaoling Liu D. H. Yuan |
| author_facet | Xiaoling Liu D. H. Yuan |
| author_sort | Xiaoling Liu |
| collection | DOAJ |
| description | We firstly construct a concrete semi-invex set which is
not invex. Basing on concept of semi-invex set, we introduce some kinds
of generalized convex functions, which include semi-(B,G)-preinvex functions, strictly semi-(B,G)-preinvex functions and explicitly semi-(B,G)-preinvex functions. Moreover, we establish relationships between our new
generalized convexity and generalized convexity introduced in the literature. With these relationships and the well-known results pertaining to
common generalized convexity, we obtain results for our new generalized
convexities. We extend the existing results in the literature. |
| format | Article |
| id | doaj-art-4da7a63693ed4e76aa433f584dafd258 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-4da7a63693ed4e76aa433f584dafd2582025-08-20T02:38:45ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/530468530468On Semi-(B,G)-Preinvex FunctionsXiaoling Liu0D. H. Yuan1Department of Mathematics, Hanshan Normal University, Chaozhou, Guangdong 521041, ChinaDepartment of Mathematics, Hanshan Normal University, Chaozhou, Guangdong 521041, ChinaWe firstly construct a concrete semi-invex set which is not invex. Basing on concept of semi-invex set, we introduce some kinds of generalized convex functions, which include semi-(B,G)-preinvex functions, strictly semi-(B,G)-preinvex functions and explicitly semi-(B,G)-preinvex functions. Moreover, we establish relationships between our new generalized convexity and generalized convexity introduced in the literature. With these relationships and the well-known results pertaining to common generalized convexity, we obtain results for our new generalized convexities. We extend the existing results in the literature.http://dx.doi.org/10.1155/2012/530468 |
| spellingShingle | Xiaoling Liu D. H. Yuan On Semi-(B,G)-Preinvex Functions Abstract and Applied Analysis |
| title | On Semi-(B,G)-Preinvex Functions |
| title_full | On Semi-(B,G)-Preinvex Functions |
| title_fullStr | On Semi-(B,G)-Preinvex Functions |
| title_full_unstemmed | On Semi-(B,G)-Preinvex Functions |
| title_short | On Semi-(B,G)-Preinvex Functions |
| title_sort | on semi b g preinvex functions |
| url | http://dx.doi.org/10.1155/2012/530468 |
| work_keys_str_mv | AT xiaolingliu onsemibgpreinvexfunctions AT dhyuan onsemibgpreinvexfunctions |