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Some fixed point theorems for compact maps and flows in Banach spaces

1970
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Transactions of the American Mathematical Society
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Let S0OE Sic S2 be convex subsets of the Banach space X, with S0 and S2 closed and Si open in S2. If / is a compact mapping of S2 into X such that U*=i/'(Si)c^ and/m(5i) u/m+1(5i)c50 for some »i>0, then/has a fixed point in S0. (This extends a result of F. E. Browder published in 1959.) Also, if {Tt : t s R*} is a continuous flow on the Banach space X, 50cSic=52 are convex subsets of X with So and S2 compact and Si open in S2, and 7*¡0(Si)c.So for some i0>0, where 7"((Si) <=S2 for all f¿ta,

doi:10.1090/s0002-9947-1970-0267432-1
fatcat:hhbt5nitqbdurnc6ukzpw7drt4