Existence of Equilibria and Fixed Points of Set-Valued Mappings on Epi-Lipschitz Sets with Weak Tangential Conditions
We prove a new result of existence of equilibria for an u.s.c. set-valued mapping F on a compact set S of Rn which is epi-Lipschitz and satisfies a weak tangential condition. Equivalently this provides existence of fixed points of the set-valued mapping x⇉F(x)-x. The main point of our result lies in...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2016-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/5671729 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832551268824907776 |
|---|---|
| author | Messaoud Bounkhel |
| author_facet | Messaoud Bounkhel |
| author_sort | Messaoud Bounkhel |
| collection | DOAJ |
| description | We prove a new result of existence of equilibria for an u.s.c. set-valued mapping F on a compact set S of Rn which is epi-Lipschitz and satisfies a weak tangential condition. Equivalently this provides existence of fixed points of the set-valued mapping x⇉F(x)-x. The main point of our result lies in the fact that we do not impose the usual tangential condition in terms of the Clarke tangent cone. Illustrative examples are stated showing the importance of our results and that the existence of such equilibria does not need necessarily such usual tangential condition. |
| format | Article |
| id | doaj-art-a42305a2b17d46a78e3ba8bb921d7c09 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-a42305a2b17d46a78e3ba8bb921d7c092025-02-03T06:01:55ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/56717295671729Existence of Equilibria and Fixed Points of Set-Valued Mappings on Epi-Lipschitz Sets with Weak Tangential ConditionsMessaoud Bounkhel0Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaWe prove a new result of existence of equilibria for an u.s.c. set-valued mapping F on a compact set S of Rn which is epi-Lipschitz and satisfies a weak tangential condition. Equivalently this provides existence of fixed points of the set-valued mapping x⇉F(x)-x. The main point of our result lies in the fact that we do not impose the usual tangential condition in terms of the Clarke tangent cone. Illustrative examples are stated showing the importance of our results and that the existence of such equilibria does not need necessarily such usual tangential condition.http://dx.doi.org/10.1155/2016/5671729 |
| spellingShingle | Messaoud Bounkhel Existence of Equilibria and Fixed Points of Set-Valued Mappings on Epi-Lipschitz Sets with Weak Tangential Conditions Journal of Function Spaces |
| title | Existence of Equilibria and Fixed Points of Set-Valued Mappings on Epi-Lipschitz Sets with Weak Tangential Conditions |
| title_full | Existence of Equilibria and Fixed Points of Set-Valued Mappings on Epi-Lipschitz Sets with Weak Tangential Conditions |
| title_fullStr | Existence of Equilibria and Fixed Points of Set-Valued Mappings on Epi-Lipschitz Sets with Weak Tangential Conditions |
| title_full_unstemmed | Existence of Equilibria and Fixed Points of Set-Valued Mappings on Epi-Lipschitz Sets with Weak Tangential Conditions |
| title_short | Existence of Equilibria and Fixed Points of Set-Valued Mappings on Epi-Lipschitz Sets with Weak Tangential Conditions |
| title_sort | existence of equilibria and fixed points of set valued mappings on epi lipschitz sets with weak tangential conditions |
| url | http://dx.doi.org/10.1155/2016/5671729 |
| work_keys_str_mv | AT messaoudbounkhel existenceofequilibriaandfixedpointsofsetvaluedmappingsonepilipschitzsetswithweaktangentialconditions |