Equilibria of nonconvex valued maps under constraints (Q764916)
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scientific article; zbMATH DE number 6015239
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Equilibria of nonconvex valued maps under constraints |
scientific article; zbMATH DE number 6015239 |
Statements
Equilibria of nonconvex valued maps under constraints (English)
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16 March 2012
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A notion of \(n\)-tangency is introduced for set-valued mappings in Banach spaces and some equilibrium theorems are given for this type of mappings. The main result is as follows. Theorem 2.3. If \(E\) is a Banach space, \(M\) is a compact and sleek \(\mathcal{L}\)-retract of \(E\) such that \(\chi(M)\neq 0\), \(\dim(M)\leq n+1\) and \(\varphi:M\to E\) is an \(n\)-tangent upper semi-continuous set-valued map, then there exists \(x_0\in M\) such that \(0\in \varphi(x_0)\).
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equilibria
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set-valued maps
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approximations
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sleek retracts
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tangent maps
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