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.
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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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Elin, M., Shoikhet, D. (2017). Fixed Points of Pseudo-Contractive Holomorphic Mappings. In: Bracci, F. (eds) Geometric Function Theory in Higher Dimension. Springer INdAM Series, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-73126-1_2
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DOI: https://doi.org/10.1007/978-3-319-73126-1_2
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