On properties of geodesic semilocal E-preinvex functions
Abstract The authors define a class of functions on Riemannian manifolds, which are called geodesic semilocal E-preinvex functions, as a generalization of geodesic semilocal E-convex and geodesic semi E-preinvex functions, and some of its properties are established. Furthermore, a nonlinear fraction...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-12-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-018-1944-z |
| _version_ | 1811307234036023296 |
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| author | Adem Kılıçman Wedad Saleh |
| author_facet | Adem Kılıçman Wedad Saleh |
| author_sort | Adem Kılıçman |
| collection | DOAJ |
| description | Abstract The authors define a class of functions on Riemannian manifolds, which are called geodesic semilocal E-preinvex functions, as a generalization of geodesic semilocal E-convex and geodesic semi E-preinvex functions, and some of its properties are established. Furthermore, a nonlinear fractional multiobjective programming is considered, where the functions involved are geodesic E-η-semidifferentiability, sufficient optimality conditions are obtained. A dual is formulated and duality results are proved by using concepts of geodesic semilocal E-preinvex functions, geodesic pseudo-semilocal E-preinvex functions, and geodesic quasi-semilocal E-preinvex functions. |
| first_indexed | 2024-04-13T09:00:38Z |
| format | Article |
| id | doaj.art-0b1696ae892d44bb8bf9715f10b939c5 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-13T09:00:38Z |
| publishDate | 2018-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-0b1696ae892d44bb8bf9715f10b939c52022-12-22T02:53:09ZengSpringerOpenJournal of Inequalities and Applications1029-242X2018-12-012018111310.1186/s13660-018-1944-zOn properties of geodesic semilocal E-preinvex functionsAdem Kılıçman0Wedad Saleh1Department of Mathematics and Institute for Mathematical Research, University Putra MalaysiaDepartment of Mathematics, Taibah UniversityAbstract The authors define a class of functions on Riemannian manifolds, which are called geodesic semilocal E-preinvex functions, as a generalization of geodesic semilocal E-convex and geodesic semi E-preinvex functions, and some of its properties are established. Furthermore, a nonlinear fractional multiobjective programming is considered, where the functions involved are geodesic E-η-semidifferentiability, sufficient optimality conditions are obtained. A dual is formulated and duality results are proved by using concepts of geodesic semilocal E-preinvex functions, geodesic pseudo-semilocal E-preinvex functions, and geodesic quasi-semilocal E-preinvex functions.http://link.springer.com/article/10.1186/s13660-018-1944-zGeneralized convexityRiemannian geometryDuality |
| spellingShingle | Adem Kılıçman Wedad Saleh On properties of geodesic semilocal E-preinvex functions Journal of Inequalities and Applications Generalized convexity Riemannian geometry Duality |
| title | On properties of geodesic semilocal E-preinvex functions |
| title_full | On properties of geodesic semilocal E-preinvex functions |
| title_fullStr | On properties of geodesic semilocal E-preinvex functions |
| title_full_unstemmed | On properties of geodesic semilocal E-preinvex functions |
| title_short | On properties of geodesic semilocal E-preinvex functions |
| title_sort | on properties of geodesic semilocal e preinvex functions |
| topic | Generalized convexity Riemannian geometry Duality |
| url | http://link.springer.com/article/10.1186/s13660-018-1944-z |
| work_keys_str_mv | AT ademkılıcman onpropertiesofgeodesicsemilocalepreinvexfunctions AT wedadsaleh onpropertiesofgeodesicsemilocalepreinvexfunctions |