Equilibria of nonconvex valued maps under constraints
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 \(0\in \varphi(x_0)\).
scientific article; zbMATH DE number 6015239