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Fixed Points of Pseudo-Contractive Holomorphic Mappings

  • Mark Elin
  • David Shoikhet
Chapter
First Online:
Part of the Springer INdAM Series book series (SINDAMS, volume 26)

Abstract

We study conditions that ensure the existence of fixed points of pseudo-contractive mappings originally considered by Browder, Kato, Kirk and Morales. Specifically we consider holomorphic pseudo-contractions on the open unit ball of a complex Banach space which in general are not necessarily bounded. As a consequence, we obtain sufficient conditions for the existence and uniqueness of the common fixed point of a semigroup of holomorphic self-mappings and study its rate of convergence to this point.

Keywords

Holomorphic maps Fixed point theory Contractive maps 

Mathematics Subject Classification

37C25 32A10 
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Notes

Acknowledgements

The work was partially supported by the European Commission under the project STREVCOMS PIRSES-2013-612669. The publication was prepared with the support of the “RUDN University Program 5-100”. Both authors are grateful to the anonymous referee for the very fruitful remarks.

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© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of MathematicsKarmielIsrael
  2. 2.Department of MathematicsHolonIsrael

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