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Fixed Points of Holomorphic Mappings: A Metric Approach

In: Handbook of Metric Fixed Point Theory

Author

Listed:
  • Tadeusz Kuczumow

    (Maria Curie-Skłodowska University)

  • Simeon Reich

    (The Technion-Israel Institute of Technology, Department of Mathematics)

  • David Shoikhet

    (ORT Braude College, Department of Applied Mathematics)

Abstract

Let X 1 and X 2 be two complex normed linear spaces and let D 1 be a domain (that is, a nonempty open connected subset) in X 1. A mapping f : D 1 → X 2 is said to be holomorphic in D 1 if it is Fréchet differentiable at each point of D 1. If D 1 and D 2 are domains in X 1 and X 2, respectively, then H(D 1, D 2) will denote the family of all holomorphic mappings from D 1 into D 2.

Suggested Citation

  • Tadeusz Kuczumow & Simeon Reich & David Shoikhet, 2001. "Fixed Points of Holomorphic Mappings: A Metric Approach," Springer Books, in: William A. Kirk & Brailey Sims (ed.), Handbook of Metric Fixed Point Theory, chapter 0, pages 437-515, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-1748-9_14
    DOI: 10.1007/978-94-017-1748-9_14
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