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.
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Dedicated to Professor Felix Browder
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Ben-El-Mechaiekh, H. Equilibria for set-valued maps on nonsmooth domains. J. fixed point theory appl. 4, 177–182 (2008). https://doi.org/10.1007/s11784-008-0074-5
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DOI: https://doi.org/10.1007/s11784-008-0074-5