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Uniform convexity of the hyperbolic metric and fixed points of holomorphic mappings in the Hilbert ball. (English) Zbl 0448.47048

MSC:
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
32F45Invariant metrics and pseudodistances
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References:
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[2] Carathéodory, C.: Über das schwarzsche lemma bei analytischen funktionen von zwei komplexen veränderlichen. Math. ann. 97, 76-98 (1926) · Zbl 52.0345.02
[3] Earle, C. J.; Hamilton, R. S.: A fixed point theorem for holomorphic mappings. Proc. symposia pure math. 16, 61-65 (1970) · Zbl 0205.14702
[4] Edelstein, M.: The construction of an asymptotic center with a fixed point property. Bull. am. Math. soc. 78, 206-208 (1972) · Zbl 0231.47029
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[8] Harris, L. A.: Act. sci. Et ind.. (1975)
[9] Harris, L. A.: Schwarz-Pick systems of pseudometrics for domains in a normed linear space. Advanced in holomorphy proc. Seminario de holomorfia, 345-406 (1979)
[10] Hayden, T. L.; Suffridge, T. J.: Fixed points of holomorphic maps in Banach spaces. Proc. am. Math. soc. 60, 95-105 (1976) · Zbl 0347.47032
[11] Hayden, T. L.; Suffridge, T. J.: Biholomorphic maps in Hilbert space have a fixed point. Pacif. J. Math. 38, 419-422 (1971) · Zbl 0229.47043
[12] Hervé, M.: Several complex variables, local theory. (1963) · Zbl 0113.29003
[13] Hille, E.; Phillips, R. S.: Functional analysis and semigroups. Amer. math. Soc. coll. Publ. 31 (1957) · Zbl 0078.10004
[14] Kijima, Y.; Takahashi, W.: A fixed point theorem for non-expansive mappings in metric space. Kodai math. Sem. rep. 21, 326-330 (1969) · Zbl 0188.55401
[15] Kirk, W. A.: A fixed point theorem for mappings which do not increase distances. Am. math. Monthly 72, 1004-1006 (1965) · Zbl 0141.32402
[16] Opial, Z.: Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull. am. Math. soc. 73, 591-597 (1967) · Zbl 0179.19902
[17] Reiffen, H. J.: Die carathéodorysche distanz und ihre zugehörige differentialmetrik. Math. ann. 161, 315-324 (1965) · Zbl 0141.08803
[18] Reiffen, H. J.: Die differential geometrischen eigenschaften der invarianten distanzfunktion von Carathéodory. Schrift math. Inst. univ. Münster 26 (1963) · Zbl 0115.16303