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Fixed points and best approximation in Menger convex metric spaces

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*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.