Skip to main content
Log in

Fixed point theorems for holomorphic mappings and operator theory in indefinite metric spaces

  • Published:
Integral Equations and Operator Theory Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

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.

    Google Scholar 

  • [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.

    Google Scholar 

  • [FV] T. Franzoni and E. Vesentini, Holomorphic Maps and Invariant Distances, North Holland, Amsterdam, 1980.

    Google Scholar 

  • [GR] K. Goebel and S. Reich, Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Marcel Dekker, New York and Basel, 1984.

    Google Scholar 

  • [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.

    Google Scholar 

  • [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.

    Google Scholar 

  • [KhS2] V. Khatskevich and V. Senderov, Powers of plus-operators, Integral Equations and Operator Theory15 (1992), 784–795.

    Google Scholar 

  • [KhSh] V. Khatskevich and D. Shoikhet, Differentiable Operators and Nonlinear Equations, Operator Theory, Vol. 66, Birkhauser Verlag, Basel, 1994.

    Google Scholar 

  • [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.

    Google Scholar 

  • [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.

    Google Scholar 

  • [KS] W. A. Kirk and R. Schöneberg, Zeros ofm-accretive operators in Banach spaces, Israel J. Math.35 (1980), 1–8.

    Google Scholar 

  • [KZ] M.A. Krasnoselskii and P.P. Zabreiko, Geometrical Methods of Nonlinear Analysis. Springer-Verlag, Berlin, 1984.

    Google Scholar 

  • [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.

    Google Scholar 

  • [R] S. Reich, On fixed point theorems obtained from existence theorems for differential equations, J. Math. Anal. Appl.54 (1976), 26–36.

    Google Scholar 

  • [RT] S. Reich and R. Torrejon, Zeros of accretive operators, Comment. Math. Univ. Carolinae21 (1980), 619–625.

    Google Scholar 

  • [S] D. Shoikhet, Some properties of Fredholm mappings in Banach analytic manifolds, Integral Equations and Operator Theory16 (1993), 430–451.

    Google Scholar 

  • [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.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01378779

1991 Mathematics Subject Classification

Navigation