Abstract
In this paper we establish several new results on the existence and uniqueness of a fixed point for holomorphic mappings and one-parameter semigroups in Banach spaces. We also present an application to operator theory on spaces with an indefinite metric.
Similar content being viewed by others
References
[C] J. Cronin, Fixed Points and Topological Degree in Nonlinear Analysis, Math. Surveys 11, AMS, Providence, R.I., 1964.
[EH] C.J. Earle and R.S. Hamilton, A fixed point theorem for holomorphic mappings, Proc. Symp. Pure Math., Vol. 16., Amer. Math. Soc., Providence, R.I., 1970, pp. 61–65.
[FV] T. Franzoni and E. Vesentini, Holomorphic Maps and Invariant Distances, North Holland, Amsterdam, 1980.
[GR] K. Goebel and S. Reich, Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Marcel Dekker, New York and Basel, 1984.
[Kh] V. Khatskevich, On an application of the contraction principle in the operator theory on spaces with indefinite metric, Funct. Anal. i Prilozen.,12 (1978), 88–89.
[KhS1] V. Khatskevich and V. Senderov, On normedJ-spaces and some classes of linear operators in these spaces (Russian), Mat. Issled.8 (1973), 56–75.
[KhS2] V. Khatskevich and V. Senderov, Powers of plus-operators, Integral Equations and Operator Theory15 (1992), 784–795.
[KhSh] V. Khatskevich and D. Shoikhet, Differentiable Operators and Nonlinear Equations, Operator Theory, Vol. 66, Birkhauser Verlag, Basel, 1994.
[Krl] M. Krein, On an application of a fixed point principle in the theory of linear mappings in spaces with an indefinite metric, Dokl. Akad. Nauk SSSR5 (1950), 180–190.
[Kr2] M. Krein, On a new application of a fixed point principle in the theory of operators on spaces with indefinite metrics, Dokl. Akad. Nauk SSSR154 (1964), 1023–1026.
[KS] W. A. Kirk and R. Schöneberg, Zeros ofm-accretive operators in Banach spaces, Israel J. Math.35 (1980), 1–8.
[KZ] M.A. Krasnoselskii and P.P. Zabreiko, Geometrical Methods of Nonlinear Analysis. Springer-Verlag, Berlin, 1984.
[Ph] R. Phillips, The extension of dual subspaces invariant under an algebra, inProc. Internat. Sympos. Linear Spaces, Jerusalem, 1960, Jerusalem Acad. Press, Oxford-London-New York-Paris, 1961, pp. 366–398.
[R] S. Reich, On fixed point theorems obtained from existence theorems for differential equations, J. Math. Anal. Appl.54 (1976), 26–36.
[RT] S. Reich and R. Torrejon, Zeros of accretive operators, Comment. Math. Univ. Carolinae21 (1980), 619–625.
[S] D. Shoikhet, Some properties of Fredholm mappings in Banach analytic manifolds, Integral Equations and Operator Theory16 (1993), 430–451.
[V] J.-P. Vigué, Points fixes d'applications holomorphes dans un produit fini de boulesunités d'espaces de Hilbert, Annali di Matematica Pura Appl. (4)137 (1984), 245–256.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Khatskevich, V., Reich, S. & Shoikhet, D. Fixed point theorems for holomorphic mappings and operator theory in indefinite metric spaces. Integr equ oper theory 22, 305–316 (1995). https://doi.org/10.1007/BF01378779
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01378779