A minimax theorem for vector-valued functions. II
We deal with the minimax problem relative to a vector-valued function f: \(X_ 0\times Y_ 0\to V\), where a partial ordering in the topological vector space V is induced by a closed and convex cone C. In the first part of this article [ibid. 60, No.1, 19-31 (1989; Zbl 0631.90077)], under suitable hypotheses, we proved that \[ Max\cup_{s\in X_ 0}Min_ wf(s,Y_ 0)\subset Min\cup_{t\in Y_ 0}Max f(X_ 0,t)+C; \] the exact meaning of the symbols is given in Section 2. In this work, we prove that, under a reasonable setting of hypotheses, the previous inclusion holds and also we have that \[ Min_ w\cup_{t\in Y_ 0}Max f(X_ 0,t)\subset Max\cup_{s\in X_ 0}Min_ wf(s,Y_ 0)-C. \]
scientific article; zbMATH DE number 4141810