Uniformly convex spaces, bead spaces, and equivalence conditions

Pasicki, Lech. "Uniformly convex spaces, bead spaces, and equivalence conditions." Czechoslovak Mathematical Journal 61.2 (2011): 383-388. <http://eudml.org/doc/196476>.

@article{Pasicki2011,
abstract = {The notion of a metric bead space was introduced in the preceding paper (L. Pasicki: Bead spaces and fixed point theorems, Topology Appl., vol. 156 (2009), 1811–1816) and it was proved there that every bounded set in such a space (provided the space is complete) has a unique central point. The bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces. It appears that normed bead spaces are identical with uniformly convex spaces. On the other hand the "metric" approach leads to new elementary conditions equivalent to the uniform convexity. The initial part of the paper contains the proof that discus spaces (they seem to have a richer structure) are identical with bead spaces.},
author = {Pasicki, Lech},
journal = {Czechoslovak Mathematical Journal},
keywords = {uniformly convex space; bead space; central point; uniformly convex space; bead space; central point},
language = {eng},
number = {2},
pages = {383-388},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Uniformly convex spaces, bead spaces, and equivalence conditions},
url = {http://eudml.org/doc/196476},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Pasicki, Lech
TI - Uniformly convex spaces, bead spaces, and equivalence conditions
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 2
SP - 383
EP - 388
AB - The notion of a metric bead space was introduced in the preceding paper (L. Pasicki: Bead spaces and fixed point theorems, Topology Appl., vol. 156 (2009), 1811–1816) and it was proved there that every bounded set in such a space (provided the space is complete) has a unique central point. The bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces. It appears that normed bead spaces are identical with uniformly convex spaces. On the other hand the "metric" approach leads to new elementary conditions equivalent to the uniform convexity. The initial part of the paper contains the proof that discus spaces (they seem to have a richer structure) are identical with bead spaces.
LA - eng
KW - uniformly convex space; bead space; central point; uniformly convex space; bead space; central point
UR - http://eudml.org/doc/196476
ER -