Finite Dimensional Chebyshev Subspaces of Lo

Authors

Aref K. Kamal, Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, PC 123, Al-Khoud, Muscat, Sultanate of Oman.

Abstract

If A is a subset of the normed linear space X, then A is said to be proximinal in X if for each xÎX there is a point y0ÎA such that the distance between x and A; d(x, A) = inf{||x-y||: yÎA}= ||x­-y0||. The element y0 is called a best approximation for x from A. If for each xÎX, the best approximation for x from A is unique then the subset A is called a Chebyshev subset of X. In this paper the author studies the existence of finite dimensional Chebyshev subspaces of Lo.

Recommended Citation

Kamal, Aref K. (2017) Finite Dimensional Chebyshev Subspaces of Lo, Sultan Qaboos University Journal For Science: Vol. 22: Iss. 1, 53-55.
DOI: https://doi.org/10.24200/squjs.vol22iss1pp53-55
Available at: https://squjs.squ.edu.om/squjs/vol22/iss1/3