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Fixed points of uniformly Lipschitzian mappings in spaces with uniformly normal structure. (English) Zbl 0526.47034

MSC:
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
46B20Geometry and structure of normed linear spaces
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References:
[1] Amir D., On Jung’s constant and related constants in normed linear spaces Pacif. J. Math. (to appear). · Zbl 0529.46011
[2] Baillon, J. B.: Quelques aspects de la théorie des pointes fixes dans LES éspaces de Banach I. Seminaire d’analyse fonctionnelle 7 (1978--1979)
[3] Baillon, J. B.; Schöneberg, R.: Asymptotic normal structure and fixed points of nonexpansive maps. Proc. am. Math. soc. 81, 257-264 (1981) · Zbl 0465.47038
[4] Bynum, W. L.: Normal structure coefficients for Banach spaces. Pacif. J. Math. 86, 427-436 (1980) · Zbl 0442.46018
[5] Downing, D.; Turett, B.: Some properties of the characteristic of convexity relating to fixed point theory. Pacif. J. Math. 104, 343-350 (1983) · Zbl 0464.47036
[6] Goebel, K.; Kirk, W. A.: A fixed point theorem for transformations whose iterates have uniform Lipschitz constant. Studia math. 47, 135-140 (1973) · Zbl 0265.47044
[7] Goebel, K.; Kirk, W. A.; Thele, R. L.: Uniformly Lipschitzian families of transformations in Banach spaces. Can. J. Math. 26, 1245-1256 (1974) · Zbl 0285.47039
[8] Kirk, W. A.: A fixed point theorem for mappings which do not increase distances. Am. math. Mon. 72, 1004-1006 (1965) · Zbl 0141.32402
[9] Kuhn, M. G.: A remark on ${\gamma}$-Lipschitzian mappings. Boll. un. Mat. ital. 1-B, 413-421 (1982) · Zbl 0517.47032
[10] Lifschitz, E. A.: Fixed point theorems for operators in strongly convex spaces. Voronez\breve{} GoS univ. Trudy math. Fak. 16, 23-28 (1975)
[11] Lim, T. C.: Fixed point theorems for uniformly Lipschitzian mappings in lp spaces. Nonlinear analysis 7, 555-563 (1983) · Zbl 0533.47049
[12] Maluta, E.: Uniformly normal structure and related coefficients. Pacif. J. Math. 111, 357-369 (1984) · Zbl 0495.46012