A remark on best coapproximation in L^\infty(\mu,X)

As a counterpart to best approximation in Banach spaces, the best coapproximation was introduced by Franchetti and Furi (1972). In this paper, we shall consider the relation between coproximinality of a nonempty subsetMof a Banach spaceXand ofC(S, M)inC(S, X).

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SOme results about best coapproximation in L P (S,X)

Analysis in Theory and Applications ◽

10.1007/s10496-010-0069-0 ◽

2010 ◽

Vol 26 (1) ◽

pp. 69-75

Author(s):

M. R. Haddadi ◽

N. Hejazjpoor ◽

H. Mazaheri

Keyword(s):

Best Coapproximation

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Best coapproximation in quotient spaces

Nonlinear Analysis ◽

10.1016/j.na.2007.03.005 ◽

2008 ◽

Vol 68 (10) ◽

pp. 3122-3126

Author(s):

H. Mazaheri

Keyword(s):

Quotient Spaces ◽

Best Coapproximation

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Best coapproximation in normed linear spaces

Monatshefte für Mathematik ◽

10.1007/bf01305855 ◽

1979 ◽

Vol 88 (1) ◽

pp. 27-44 ◽

Cited By ~ 18

Author(s):

Pier Luigi Papini ◽

Ivan Singer

Keyword(s):

Linear Spaces ◽

Normed Linear Spaces ◽

Best Coapproximation

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Proximinality and co-proximinality in metric linear spaces

Annales Universitatis Mariae Curie-Sklodowska sectio A – Mathematica ◽

10.17951/a.2015.69.1.83 ◽

2015 ◽

Vol 69 (1) ◽

pp. 83

Author(s):

T. W. Narang ◽

Sahil Gupta

Keyword(s):

Best Approximation ◽

Existence And Uniqueness ◽

Linear Spaces ◽

Normed Linear Spaces ◽

Best Coapproximation ◽

Uniqueness Of Best Approximation

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.

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