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Semi-Lipschitz Functions and Best Approximation in Quasi-Metric Spaces

✍ Scribed by Salvador Romaguera; Manuel Sanchis

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 128 KB
Volume: 103
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1999.3439

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✦ Synopsis

We show that the set of semi-Lipschitz functions, defined on a quasi-metric space (X, d ), that vanish at a fixed point x 0 # X can be endowed with the structure of a quasi-normed semilinear space. This provides an appropriate setting in which to characterize both the points of best approximation and the semi-Chebyshev subsets of quasi-metric spaces. We also show that this space is bicomplete.

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## Abstract In this paper the concepts of strictly convex and uniformly convex normed linear spaces are extended to metric linear spaces. A relationship between strict convexity and uniform convexity is established. Some existence and uniqueness theorems on best approximation in metric linear space