Best Approximation in a Class of Normed Spaces with Star-Shaped Cone
- 31 August 2006
- journal article
- research article
- Published by Informa UK Limited in Numerical Functional Analysis and Optimization
- Vol. 27 (3-4), 411-436
- https://doi.org/10.1080/01630560600686231
Abstract
We examine best approximation by closed sets in a class of normed spaces with star-shaped cones. It is assumed that the norm on the space X under consideration is generated by a star-shaped cone. First, we study best approximation by downward and upward sets, and then we use the results obtained as a tool for examination of best approximation by an arbitrary closed set.Keywords
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