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Existence of fixed points for asymptotically nonexpansive type actions of semigroups

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Abstract

We prove the existence of common fixed points for reversible semitopological semigroups acting asymptotically nonexpansive type on nonempty compact convex sets in the context of locally convex spaces. This answers a problem raised by Lau (Fixed Point Theory Appl, 2010), for an asymptotically nonexpansive type action.

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Acknowledgements

The authors would like to thank the anonymous reviewer for his or her thoughtful review of the manuscript, constructive comments and suggesting the idea of Theorem 2.7.

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Authors and Affiliations

  1. Department of Mathematics, University of Kurdistan, 416 , Sanandaj, Iran

    S. Saeidi

  2. Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran

    F. Golkar & A. M. Forouzanfar

Authors
  1. S. Saeidi
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  2. F. Golkar
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  3. A. M. Forouzanfar
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Correspondence to S. Saeidi.

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Dedicated to Professor Anthony To-Ming Lau.

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Saeidi, S., Golkar, F. & Forouzanfar, A.M. Existence of fixed points for asymptotically nonexpansive type actions of semigroups. J. Fixed Point Theory Appl. 20, 72 (2018). https://doi.org/10.1007/s11784-018-0548-z

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  • DOI: https://doi.org/10.1007/s11784-018-0548-z

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