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 semigroupMathematics Subject Classification
Primary 47H10 Secondary 20M30 47H09 47H20Notes
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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