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Existence of fixed points on compact epilipschitz sets without invariance conditions
Fixed Point Theory and Applications volume 2005, Article number: 603074 (2005)
Abstract
We provide a new result of existence of equilibria of a single-valued Lipschitz function 
on a compact set 
of 
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 
. The main point of our result lies in the fact that we do not impose that 
is an "inward vector" for all point 
of the boundary of 
. Some extensions of the existence of equilibria result are also discussed for continuous functions and set-valued maps.
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Kamenskii, M., Quincampoix, M. Existence of fixed points on compact epilipschitz sets without invariance conditions. Fixed Point Theory Appl 2005, 603074 (2005). https://doi.org/10.1155/FPTA.2005.267
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DOI: https://doi.org/10.1155/FPTA.2005.267