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Best approximation in metric spaces

Narang T. D., Gupta S.

Fasciculi Mathematici

2017

Nr 58

113--121

The aim of this paper is to prove some results on the existence and uniqueness of elements of best approximation and continuity of the metric projection in metric spaces. For a subset M of a metric space (X, d), the nature of set of those points of X which have at most one best approximation in M has been discussed. Some equivalent conditions under which an M-space is strictly convex have also been given in this paper.