Fixed points and best approximation in Menger convex metric spaces

Ismat Beg and Mujahid Abbas

Address.
Ismat Beg, Department of Mathematics, Lahore University of Management Sciences, 54792 Lahore, Pakistan

Mujahid Abbas Department of Mathematics, Covernment Post Graduate College, Sahiwal, Pakistan

E-mail. ibeg@lums.edu.pk

Abstract.
We obtain necessary conditions for the existence of fixed point and approximate fixed point of nonexpansive and quasi nonexpansive maps defined on a compact convex subset of a uniformly convex complete metric space. We obtain results on best approximation as a fixed point in a strictly convex metric space.

AMSclassification. 47H09, 47H10, 47H19, 54H25

Keywords. Fixed point, convex metric space, uniformly convex metric space, strictly convex metric space, best approximation, nonexpansive map.