### Impacto

Mendoza Casas, José and Pakhrou, Tijani
(2007)
*Best simultaneous approximation in L-1 (mu, X).*
Journal of Approximation Theory, 145
(2).
pp. 212-220.
ISSN 0021-9045

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Official URL: http://www.sciencedirect.com/science/article/pii/S0021904506001687

## Abstract

Let X be a Banach space, (Omega, Sigma, mu) a finite measure space, and L-1 (mu, X) the Banach space of X-valued Bochner mu-integrable functions defined on Omega endowed with its usual norm. Let us suppose that Sigma(0) is a sub-sigma-algebra of Sigma, and let mu(0) be the restriction of mu to Sigma(0). Given a natural number n, let N be a monotonous norm in R-n. It is shown that if X is reflexive then L-1 (mu(0), X) is N-simultaneously proximinal in L-1 (mu, X) in the sense of Fathi et al. [Best simultaneous approximation in L-p(I, E), J. Approx. Theory 116 (2002), 369-379]. Some examples and remarks related with N-simultaneous proximinality are also given.

Item Type: | Article |
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Uncontrolled Keywords: | Banach space. |

Subjects: | Sciences > Mathematics > Differential geometry |

ID Code: | 16848 |

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Deposited On: | 24 Oct 2012 08:44 |

Last Modified: | 07 Feb 2014 09:36 |

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