Some inequalities for the horosphere function and hyperbolically nonexpansive mappings on the Hilbert ball
Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 1, Tome 45 (2012), pp. 75-93.

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M. Elin; M. Levenshtein; S. Reich; D. Shoikhet. Some inequalities for the horosphere function and hyperbolically nonexpansive mappings on the Hilbert ball. Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 1, Tome 45 (2012), pp. 75-93. http://geodesic.mathdoc.fr/item/CMFD_2012_45_a5/

[1] Krasnoselskii M. A., Vainikko G. M., Zabreiko P. P., Rutitskii Ya. B., Stetsenko V. Ya., Priblizhennoe reshenie operatornykh uravnenii, Nauka, M., 1969 | MR

[2] Cowen C. C., MacCluer B. D., Composition operators on spaces of analytic functions, CRC Press, Boca Raton, 1995 | MR | Zbl

[3] Cowen C. C., Pommerenke Ch., “Inequalities for angular derivative of an analytic function in the unit disk”, J. Lond. Math. Soc., 26 (1982), 271–289 | DOI | MR | Zbl

[4] Dineen S., The Schwartz lemma, Clarendon Press, Oxford, 1989 | MR | Zbl

[5] Earle C. J., Hamilton R. S., “A fixed point theorem for holomorphic mappings”, Proc. Symp. Pure Math., 16 (1970), 61–65 | MR | Zbl

[6] Elin M., Reich S., Shoikhet D., “Asymptotic behavior of semigroups of $\rho$-nonexpansive and holomorphic mappings on the Hilbert ball”, Ann. Mat. Pura Appl. (4), 181 (2002), 501–526 | DOI | MR | Zbl

[7] Elin M., Reich S., Shoikhet D., Complex dynamical systems and the geometry of domains in Banach spaces, Dissertationes Math. (Rozprawy Mat.), 427, 2004 | MR | Zbl

[8] Franzoni T., Vesentini E., Holomorphic maps and invariant distances, North-Holland, Amsterdam, 1980 | MR | Zbl

[9] Goebel K., Reich S., Uniform convexity, hyperbolic geometry, and nonexpansive mappings, Marcel Dekker, New York–Basel, 1984 | MR

[10] Goebel K., Sȩkowski T., Stachura A., “Uniform convexity of the hyperbolic metric and fixed points of holomorphic mappings in the Hilbert ball”, Nonlinear Anal., 4 (1980), 1011–1021 | DOI | MR | Zbl

[11] Hervé M., Several complex variables: local theory, Bombay and Oxford Univ. Press, London, 1963 | MR

[12] Hervé M., Analyticity in infinite dimensional spaces, Walter de Gruyter, Berlin, 1989 | MR | Zbl

[13] Kaashoek M. A., West T. T., “Locally compact monothetic semi-algebras”, Proc. Lond. Math. Soc., 18 (1968), 428–438 | DOI | MR | Zbl

[14] Khatskevich V., Reich S., Shoikhet D., “Fixed point theorems for holomorphic mappings and operator theory in indefinite metric spaces”, Integral Equations Operator Theory, 22 (1995), 305–316 | DOI | MR | Zbl

[15] Krantz Steven G., “The Schwarz lemma at the boundary”, Complex Var. Elliptic Equ., 56 (2011), 455–468 | DOI | MR | Zbl

[16] Kuczumow T., Reich S., Shoikhet D., Fixed points of holomorphic mappings: a metric approach, Kluwer, Dordrecht, 2001 | MR | Zbl

[17] Lyubich Yu., Zemánek J., “Precompactness in the uniform ergodic theory”, Studia Math., 112 (1994), 89–97 | MR | Zbl

[18] MacCluer B. D., “Iterates of holomorphic self-maps of the unit ball in $\mathbb C^n$”, Michigan Math. J., 30 (1983), 97–106 | DOI | MR | Zbl

[19] Osserman R., “A sharp Schwarz inequality on the boundary”, Proc. Amer. Math. Soc., 128 (2000), 3513–3517 | DOI | MR | Zbl

[20] Pommerenke Ch., Boundary behavior of conformal maps, Springer, New York–Berlin–Heidelberg, 1992 | MR | Zbl

[21] Reich S., Shoikhet D., “Semigroups and generators on convex domains with the hyperbolic metric”, Atti Acad. Naz. Lincei., 8 (1997), 231–250 | MR | Zbl

[22] Reich S., Shoikhet D., “The Denjoy–Wolff theorem”, Ann. Univ. Mariae Curie-Skłodowska, 51 (1997), 219–240 | MR | Zbl

[23] Reich S., Shoikhet D., “The Denjoy–Wolff theorem”, Math. Encyclopedia, Supplement 3, Kluwer Academic Publishers, 2002, 121–123

[24] Reich S., Shoikhet D., Nonlinear semigroups, fixed points, and geometry of domains in Banach spaces, Imperial College Press, London, 2005 | MR | Zbl

[25] Rudin W., Function theory in the unit ball of $\mathbb C^n$, Springer, Berlin, 1980 | MR | Zbl

[26] Shapiro J. H., Composition operators and classical function theory, Springer, Berlin, 1993 | MR

[27] Shoikhet D., Semigroups in geometrical function theory, Kluwer, Dordrecht, 2001 | MR | Zbl

[28] Shoikhet D., A generalized version of the Earle-Hamilton fixed point theorem for the Hilbert ball, 2011, arXiv: 1105.2877 | MR

[29] Stachura A., “Iterates of holomorphic self-maps of the unit ball in Hilbert space”, Proc. Amer. Math. Soc., 93 (1985), 88–90 | DOI | MR | Zbl

[30] Świȩch A., “Spectral characterization of operators with precompact orbit”, Studia Math., 96 (1991), 277–282 | MR