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One-local retract and common fixed point for commuting mappings in metric spaces. (English) Zbl 0882.54039
The author proves some fixed point theorems for non-expansive mappings. He also proves a fixed point theorem for commutative nonexpansive mappings when the metric space is bounded with compact and normal convexity structure.

54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
Full Text: DOI
[1] Khamsi, M.A.: On the weak*-fixed point property. Contemporary math. 85, 325-337 (1989)
[2] Belluce, L.P.; Kirk, W.A.: Nonexpansive mappings and fixed points in Banach spaces. Illinois J. Math. 11, 469-474 (1967) · Zbl 0149.10702
[3] Lim, T.C.: Characterizations of normal structure. Proc. am. Math. soc. 43, 313-319 (1974) · Zbl 0284.47031
[4] Penot, J.: Fixed point theorems without convexity. Bull. soc. Math. France 60, 129-152 (1979) · Zbl 0454.47044
[5] Baillon, J.B.: Nonexpansive mappings and hyperconvex space. Contemporary math. 72, 11-19 (1988)
[6] Khamsi, M.A.: Etude de la propriété du point fixe dans LES espaces de Banach et LES espaces métriques. Thése de doctorat de l’université Paris VI (1987) · Zbl 0611.46018
[7] Kirk, W.A.: A fixed point theorem for mappings which do not increase distances. Am. math. Soc. monthly 72, 1004-1006 (1965) · Zbl 0141.32402
[8] Kirk, W.A.: Nonexpansive mappings in metric and Banach spaces. Rc. semin. Mat. fis. Milano 61, 133-144 (1981) · Zbl 0519.54029
[9] BUBER T. & KIRK W.A., Convexity structures and the existence of minimal sets, preprint.
[10] Aksoy, A.G.; Khamsi, M.A.: Nonstandard methods in fixed point theory. (1990) · Zbl 0713.47050
[11] Goebel, K.; Kirk, W.A.: Topics in metric fixed point theory. (1990) · Zbl 0708.47031
[12] Kijima, Y.; Takahashi, W.: A fixed point theorem for nonexpansive mappings in metric space. Kodai. math. Sem. rep. 21, 326-330 (1969) · Zbl 0188.55401