Journal of Convex Analysis 20 (2013), No. 3, 753--761
Copyright Heldermann Verlag 2013
Existence Theorems for Generalized Asymptotically Nonexpansive Mappings in Uniformly Convex Metric Spaces
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
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.
Keywords: Generalized asymptotically nonexpansive mappings, uniformly convex metric spaces, uniformly convex hyperbolic spaces, CAT(0).
MSC: 47H09, 47H10
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