Some fixed point theorems for compact maps and flows in Banach spaces.
Some fixed point theorems for compact maps and flows in Banach spaces.
Let ${S_0} \subset {S_1} \subset {S_2}$ be convex subsets of the Banach space X, with ${S_0}$ and ${S_2}$ closed and ${S_1}$ open in ${S_2}$. If f is a compact mapping of ${S_2}$ into X such that $\cup _{j = 1}^m{f^j}({S_1}) \subset {S_2}$ and ${f^m}({S_1}) \cup {f^{m + 1}}({S_1}) \subset {S_0}$ …