A Note on Ball Proximinality
نویسندگان
چکیده
منابع مشابه
Stability of ball proximinality
In this paper, we show that if E is an order continuous Köthe function space and Y is a separable subspace ofX, then E(Y ) is ball proximinal in E(X) if and only if Y is ball proximinal in X. As a consequence, E(Y ) is proximinal in E(X) if and only if Y is proximinal in X. This solves an open problem of Bandyopadhyay, Lin and Rao. It is also shown that if E is a Banach lattice with a 1-uncondi...
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A known, and easy to establish, fact in Best Approximation Theory is that, if the unit ball of a subspace G of a Banach space X is proximinal in X, then G itself is proximinal in X. We are concerned in this article with the reverse implication, as the knowledge of whether the unit ball is proximinal or not is useful in obtaining information about other problems. We show, by constructing a count...
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As a counterpart to best approximation, the concept of best coapproximation was introduced in normed linear spaces by C. Franchetti and M. Furi in 1972. Subsequently, this study was taken up by many researchers. In this paper, we discuss some results on the existence and uniqueness of best approximation and best coapproximation when the underlying spaces are metric linear spaces. A new kind of ...
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ژورنال
عنوان ژورنال: Applied Mathematics
سال: 2020
ISSN: 2152-7385,2152-7393
DOI: 10.4236/am.2020.1111081