On Continuity of the best Approximation Map and Fixed Point Theorems

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Authors

  • Department of Mathematics, Guru Nanak Dev University, Amritsar-143005 ,IN
  • Department of Mathematics, Dr. B.R. Ambedkar National Institute of Technology, Jalandhar-144011 ,IN

Keywords:

Core Point, Convex Metric Space, Best Approximation, Proximinal, Convex and Approximatively Compact Set.

Abstract

The paper contains some results on the continuity of the best approximation map in normed linear spaces, on fixed point of a continuous nowhere normal outward map in metric linear spaces, and on fixed point of a nonexpansive map in the case of metric spaces. The proved results generalize and extend the earlier known results on the subject.