Some asymptotic fixed point theorems

Nussbaum, Roger D.

doi:10.1090/S0002-9947-1972-0310719-6

Some asymptotic fixed point theorems
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Trans. Amer. Math. Soc. 171 (1972), 349-375 Request permission

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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