Open AccessBest Approximation in Metric Spaces
Author(s) -
T. D. Narang,
Sahil Gupta
Publication year - 2017
Publication title -
fasciculi mathematici
Language(s) - English
Resource type - Journals
ISSN - 0044-4413
DOI - 10.1515/fascmath-2017-0008
Subject(s) - mathematics , metric (unit) , convex metric space , uniqueness , metric space , injective metric space , space (punctuation) , projection (relational algebra) , regular polygon , intrinsic metric , product metric , set (abstract data type) , pure mathematics , uniform continuity , equivalence of metrics , mathematical analysis , computer science , algorithm , geometry , operations management , economics , programming language , operating system
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.