Some new asymptotic fixed point theorems.
For a continuous self mapping f of a locally convex topological vector space which is locally compact (i.e., f maps a neighborhood of each point into a relatively compact set), it is shown that a sufficient condition for the existence of a fixed point is the existence of a compact attractor K(0) such that each orbit under f has a point of K(0) in its closure. The proof is based upon the circle of ideas of the Lefschetz fixed point theorem.
Browder
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Department of Mathematics, University of Chicago, Chicago, Illinois 60637.