Some subspaces simultaneously proximinal

Purpose - In this paper the aim is to present some subspace simultaneously proximinal in the Banach space L1(μ, X) of X-valued Bochner μ-integrable functions.Design methodology approach - By lower semicontinuity and compactness the existence of best simultaneous approximation is obtained.Findings -...

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Vydáno v:Kybernetes Ročník 41; číslo 1/2; s. 108 - 115
Hlavní autor: Pakhrou, Tijani
Médium: Journal Article
Jazyk:angličtina
Vydáno: London Emerald Group Publishing Limited 01.01.2012
Témata:
Algebra
Approximation
Banach space
Banach spaces
Constrictions
Mathematical analysis
Mathematical functions
Methodology
Studies
Subspaces
Simultaneous approximation
Best approximation
Mathematics
Geometry and structure of normed linear spaces
Approximations and expansions
Chebyshev systems
ISSN:0368-492X, 1758-7883
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Shrnutí:Purpose - In this paper the aim is to present some subspace simultaneously proximinal in the Banach space L1(μ, X) of X-valued Bochner μ-integrable functions.Design methodology approach - By lower semicontinuity and compactness the existence of best simultaneous approximation is obtained.Findings - If Y is a reflexive subspace of a Banach space X, then L1(μ, Y) is simultaneously proximinal in L1(μ, X). Furthermore, if X is reflexive and μ0 is the restriction of μ to a sub-σ-algebra, then L1(μ0, X) is simultaneously proximinal in L1(μ, X).Practical implications - Given a finite number of points in the Banach space X, is about finding a point in the subspace Y⊂X that comes close to all this points.Originality value - By the property of reflexivity two types subspaces simultaneously proximinal in L1(μ, X) are obtained.
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ISSN:0368-492X
1758-7883
DOI:10.1108/03684921211213142