Geodesic
Fixed points and best approximation in Menger convex metric spaces
Archivum mathematicum, Tome 41 (2005) no. 4, pp. 389-397

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We obtain necessary conditions for the existence of fixed point and approximate fixed point of nonexpansive and quasi nonexpansive maps defined on a compact convex subset of a uniformly convex complete metric space. We obtain results on best approximation as a fixed point in a strictly convex metric space.
Classification : 47H09, 47H10, 54H25
Keywords: fixed point; convex metric space; uniformly convex metric space; strictly convex metric space; best approximation; nonexpansive map 
@article{ARM_2005__41_4_a3,
     author = {Beg, Ismat and Abbas, Mujahid},
     title = {Fixed points and best approximation in {Menger} convex metric spaces},
     journal = {Archivum mathematicum},
     pages = {389--397},
     publisher = {mathdoc},
     volume = {41},
     number = {4},
     year = {2005},
     mrnumber = {2195492},
     zbl = {1109.47047},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2005__41_4_a3/}
}
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Beg, Ismat; Abbas, Mujahid. Fixed points and best approximation in Menger convex metric spaces. Archivum mathematicum, Tome 41 (2005) no. 4, pp. 389-397. http://geodesic.mathdoc.fr/item/ARM_2005__41_4_a3/