Geodesic
Relative Chebyshev Centers in L∞(μ,X)
Journal of convex analysis, Tome 21 (2014) no. 2, pp. 307-316.

Voir la notice de l'article provenant de la source Heldermann Verlag

Let $X$ be a Banach space and $Y$ a weakly $\mathcal{K}$-analytic subspace of $X$. In this paper we study the simultaneous proximinality in the space $L_\infty(\mu,X)$. In this sense we have proved that $L_\infty(\mu,Y)$ is simultaneously proximinal in $L_\infty(\mu,X)$ if, and only if, $Y$ is simultaneously proximinal in $X$. 
@article{JCA_2014_21_2_JCA_2014_21_2_a0,
     author = {T. Pakhrou},
     title = {Relative {Chebyshev} {Centers} in {L\protect\textsubscript{\ensuremath{\infty}}(\ensuremath{\mu},X)}},
     journal = {Journal of convex analysis},
     pages = {307--316},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2014},
     url = {http://geodesic.mathdoc.fr/item/JCA_2014_21_2_JCA_2014_21_2_a0/}
}
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T. Pakhrou. Relative Chebyshev Centers in L∞(μ,X). Journal of convex analysis, Tome 21 (2014) no. 2, pp. 307-316. http://geodesic.mathdoc.fr/item/JCA_2014_21_2_JCA_2014_21_2_a0/