Open Access

Existence of fixed points on compact epilipschitz sets without invariance conditions

Fixed Point Theory and Applications20052005:603074

Received: 4 April 2005

Published: 25 October 2005


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.

Authors’ Affiliations

Voronezh State University, Voronezh, Russia
Laboratoire de Mathématiques, Unité CNRS UMR 6205, Université de Bretagne Occidentale, Brest, France


© Kamenskii and Quincampoix 2005