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.

Keywords

Semigroup action asymptotically nonexpansive reversible semitopological semigroup 

Mathematics Subject Classification

Primary 47H10 Secondary 20M30 47H09 47H20 
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Notes

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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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KurdistanSanandajIran
  2. 2.Department of Mathematics, Faculty of Mathematical Sciences and ComputerShahid Chamran University of AhvazAhvazIran

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