A New Minimax Theorem for Linear Operators
Keywords:
Minimax, Banach spaces, linear operatorsAbstract
The aim of this note is to prove the following minimax theorem which generalizes a result by B.Ricceri and extends a previous result of the author: let be a infinite-dimensional Banach space, be a Banach space, be aconvex subset of whose interior is non-empty for the weak topology on bounded sets, ∆ a finite-dimensional convex compact subset of be a continuous convex coercive map, and
, φ R ∆ Raconvex continuous function. Assume moreover that ∆ contains at most one compact operator. Then
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