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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Some asymptotic fixed point theorems


Author: Roger D. Nussbaum
Journal: Trans. Amer. Math. Soc. 171 (1972), 349-375
MSC: Primary 47H10
MathSciNet review: 0310719
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Abstract: By an asymptotic fixed point theorem we mean a theorem in functional analysis in which the existence of fixed points of a map $ f$ is established with the aid of assumptions on the iterates $ {f^n}$ of $ f$. We prove below some new theorems of this type, and we obtain as corollaries results of F. E. Browder, G. Darbo, R. L. Frum-Ketkov, W. A. Horn and others. We also state a number of conjectures about fixed point theorems at the end of the paper.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0310719-6
PII: S 0002-9947(1972)0310719-6
Keywords: Fixed points, asymptotic fixed point theorems, fixed point index, generalized Lefschetz number, measure of noncompactness, compact map, $ k$-set-contraction
Article copyright: © Copyright 1972 American Mathematical Society