Journal of Fixed Point Theory and Applications

, Volume 4, Issue 2, pp 177–182

Equilibria for set-valued maps on nonsmooth domains


DOI: 10.1007/s11784-008-0074-5

Cite this article as:
Ben-El-Mechaiekh, H. J. fixed point theory appl. (2008) 4: 177. doi:10.1007/s11784-008-0074-5


A set-valued map defined on a compact lipschitzian retract of a normed space with nontrivial Euler characteristic and satisfying (i) a strong graph approximation property and (ii) a tangency condition expressed in terms of Clarke’s tangent cone, admits an equilibrium. This result extends in a simple way known solvability theorems to a large class of nonconvex set-valued maps defined on nonsmooth domains.


Equilibria strongly approachable set-valued maps nonsmooth domains approximative absolute neighborhood retracts lipschitzian retracts Clarke’s tangent cone Euler characteristic trivial shape 

Mathematics Subject Classification (2000).

Primary 05C38, 15A15 Secondary 05A15, 15A18 

Copyright information

© Birkhaeuser 2008

Authors and Affiliations

  1. 1.Department of MathematicsBrock UniversitySaint CatharinesCanada

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