منابع مشابه
Strong proximinality and intersection properties of balls in Banach spaces
We investigate a variation of the transitivity problem for proximinality properties of subspaces and intersection properties of balls in Banach spaces. For instance, we prove 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 strongly proximinal in X. Towards this, we prove that a finite co-dimensional proxi...
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We characterize finite-dimensional normed linear spaces as strongly proximinal subspaces in all their superspaces. A connection between upper Hausdorff semi-continuity of metric projection and finite dimensionality of subspace is given.
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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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Let X be a complete CAT(0) space with the geodesic extension property and Alexandrov curvature bounded below. It is shown that if C is a closed subset of X , then the set of points of X which have a unique nearest point in C is Gδ and of the second Baire category inX. If, in addition,C is bounded, then the set of points ofX which have a unique farthest point in C is dense in X. A proximity resu...
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For a closed subspace Y of a Banach space X, we define a separably determined property for Y in X. Let (P) be either proximinality or strong 1 1 2 -ball property and if (P) is separably determined for Y in X, then we prove that L1(μ, Y ) has the same property (P) in L1(μ,X). For an M -embedded space X, we give a class of elements in L1(μ,X ∗∗) having best approximations from L1(μ,X). We also pr...
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ژورنال
عنوان ژورنال: Revista Matemática Complutense
سال: 2001
ISSN: 1988-2807,1139-1138
DOI: 10.5209/rev_rema.2001.v14.n1.17047