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A maximum principle
Published online by Cambridge University Press: 09 April 2009
Abstract
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Let K be a nonempty compact set in a Hausdorff locally convex space, and F a nonempty family of upper semicontinuous convex-like functions from K into [–∞, ∞). K is partially ordered by F in a natural manner. It is shown among other things that each isotone, upper semicontinuous and convex-like function g: K → [ – ∞, ∞) attains its K-maximum at some extreme point of K which is also a maximal element of K.
Subject classification (Amer. Math. Soc. (MOS) 1970): primary 46 A 40.
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- Copyright © Australian Mathematical Society 1979
References
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