Fixed point, approximate fixed point and Kantorovich-Rubinstein maximum principle in convex metric spaces



We obtain necessary conditions for the existence of fixed point and approximate fixed point of nonexpansive and asymptotically nonexpansive maps defined on a closed bounded convex subset of a uniformly convex complete metric space and study the structure of the set of fixed points. We construct Mann type iterative sequences in convex metric space and study its convergence. As a consequence of fixed point results, we prove best approximation results. We also prove Kantorovich-Rubinstein maximum principle in convex metric spaces.


Fixed point Convex metric space Uniformly convex metric space Best approximation Kantorovich-Rubinstein maximum principle 

Mathematics Subject Classification (2000)

47H09 47H10 54H25 49J35 30C80 


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Copyright information

© KSCAM and Springer-Verlag 2008

Authors and Affiliations

  1. 1.Centre for Advanced Studies in MathematicsLahore University of Management SciencesLahorePakistan

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