Article

Journal of Fixed Point Theory and Applications

, Volume 4, Issue 2, pp 177-182

First online:

Equilibria for set-valued maps on nonsmooth domains

  • Hichem Ben-El-MechaiekhAffiliated withDepartment of Mathematics, Brock University Email author 

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Abstract.

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.

Keywords.

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