منابع مشابه
Transitivity of various notions of proximinality in Banach spaces
We derive transitivity of various degrees of proximinality in Banach spaces. When the transitivity does not carry forward to the bigger space we investigate these properties under some additional assumptions of the intermediate space. For instance, we show that if Z ⊆ Y ⊆ X where Z is a finite co-dimensional subspace of X which is strongly proximinal in Y and Y is an M-ideal in X then Z is stro...
متن کاملOn the Proximinality of Ridge Functions
Using two results of Garkavi, Medvedev and Khavinson [7], we give sufficient conditions for proximinality of sums of two ridge functions with bounded and continuous summands in the spaces of bounded and continuous multivariate functions respectively. In the first case, we give an example which shows that the corresponding sufficient condition cannot be made weaker for some subsets of Rn. In the...
متن کاملStability 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...
متن کاملProximinality and co-proximinality in metric linear spaces
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 ...
متن کاملOn transitivity of pronormality
This article is dedicated to soluble groups, in which pronormality is a transitive relation. Complete description of such groups is obtained.
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1987
ISSN: 0021-9045
DOI: 10.1016/0021-9045(87)90083-9