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A convexity in metric space and nonexpansive mappings. I. (English) Zbl 0268.54048

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
54E35 Metric spaces, metrizability
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[1] BROWDER, F. E., Nonexpansive nonlinear operators in a Banach space. Proc. Nat. Acad. Sci. U. S. A. 54 (1965), 1041-1044. · Zbl 0128.35801
[2] DAY, M. M., Amenable semigroup. Illinois J. Math. 1 (1957), 509-544 · Zbl 0078.29402
[3] DAY, M. M., Fixed point theorems for compact convex sets. Illinois J. Math. (1961), 585-590. · Zbl 0097.31705
[4] DE MARR, R., Common fixed-points for commuting contraction mappings. Pacifi J. Math. 13 (1963), 1139-1141. · Zbl 0191.14901
[5] DUNFORD, N., AND J. T. SCHWARTZ, Linear operators, Part 1. Interscience, Ne York (1958).
[6] KIRK, W. A., A fixed point theorem for mappings which do not increase dis tances. Amer. Math. Monthly 72 (1965), 1004-1006. · Zbl 0141.32402
[7] TAKAHASHI, W., Fixed point theorem for amenable semigroup of nonexpansiv mappings. Kodai Math. Sem. Rep. 21 (1969), 383-386. · Zbl 0197.11805
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