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Fixed Points of Pseudo-Contractive Holomorphic Mappings

  • Mark Elin
  • David Shoikhet
Chapter
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 

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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Copyright information

© 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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