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

Article

Abstract

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.

Keywords

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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