Existence of fixed points on compact epilipschitz sets without invariance conditions
We provide a new result of existence of equilibria of a single-valued Lipschitz function f on a compact set K of â„Ân which is locally the epigraph of a Lipschitz functions (such a set is called epilipschitz set). Equivalently this provides existence of fixed points of the map x↦x−f(x)....
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2005-10-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://dx.doi.org/10.1155/FPTA.2005.267 |
| Summary: | We provide a new result of existence of equilibria of a single-valued Lipschitz function f on a compact set K of â„Ân which is locally the epigraph of a Lipschitz functions (such a set is called epilipschitz set). Equivalently this provides existence of fixed points of the map x↦x−f(x). The main point of our result lies in the fact that we do not impose that f(x) is an “inward vector†for all point x of the boundary of K. Some extensions of the existence of equilibria result are also discussed for continuous functions and set-valued maps. |
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| ISSN: | 1687-1820 1687-1812 |