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Some problems and results in fixed point theory. (English) Zbl 0531.47048
In Atti Accad. Naz. Lincei, VIII. Ser. Rend. Cl. Sci. Fis. Mat. Nat. 57, 194-198 (1975; Zbl 0329.47019) the author posed ten problems on the fixed point theory of nonexpansive mappings. In the Altgeld book (University of Illinois Functional Analysis Seminar, 1975/6, pp. 1-12) he added four further problems. In the present article the author reports on the status of these problems. (Nine of them have been solved while four seem to remain open.) In addition, he discusses related results and he formulates two new problems on holomorphic maps in the Hilbert ball.
Reviewer: Chr.Fenske

MSC:
47H09Mappings defined by “shrinking” properties
47H20Semigroups of nonlinear operators