Abstract

We prove the fixed point property for generalized asymptotically nonexpansive mappings in uniformly convex metric spaces by using the concept of asymptotic center. We also discuss some fixed point theorems in uniformly convex metric spaces. Our results can be applied to obtain the existence of a fixed point of a generalized asymptotically nonexpansive mapping in both uniformly convex hyperbolic spaces and CAT(0) spaces.

Author information

Contact details are reproduced from the original publication and may be historical.

Withun Phuengrattana

Dept. of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

withun_ph@yahoo.com

Suthep Suantai

Materials Science Research Center, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

suthep.s@cmu.ac.th

Keywords

  • Generalized asymptotically nonexpansive mappings
  • uniformly convex metric spaces
  • uniformly convex hyperbolic spaces
  • CAT(0)

Mathematics Subject Classification

47H09, 47H10

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Suggested citation

W. Phuengrattana, S. Suantai. “Existence Theorems for Generalized Asymptotically Nonexpansive Mappings in Uniformly Convex Metric Spaces.” Journal of Convex Analysis 20 (2013), No. 3, 753–761. https://doi.org/10.68381/jca20042

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Published by Heldermann Verlag, 2013. Rights now held by Banach Press LLC.