On the fixed points of nonexpansive mappings in direct sums of Banach spaces

Andrzej Wiśnicki. "On the fixed points of nonexpansive mappings in direct sums of Banach spaces." Studia Mathematica 207.1 (2011): 75-84. <http://eudml.org/doc/285623>.

@article{AndrzejWiśnicki2011,
abstract = {We show that if a Banach space X has the weak fixed point property for nonexpansive mappings and Y has the generalized Gossez-Lami Dozo property or is uniformly convex in every direction, then the direct sum X ⊕ Y with a strictly monotone norm has the weak fixed point property. The result is new even if Y is finite-dimensional.},
author = {Andrzej Wiśnicki},
journal = {Studia Mathematica},
keywords = {fixed point property; direct sum; nonexpansive mapping},
language = {eng},
number = {1},
pages = {75-84},
title = {On the fixed points of nonexpansive mappings in direct sums of Banach spaces},
url = {http://eudml.org/doc/285623},
volume = {207},
year = {2011},
}

TY - JOUR
AU - Andrzej Wiśnicki
TI - On the fixed points of nonexpansive mappings in direct sums of Banach spaces
JO - Studia Mathematica
PY - 2011
VL - 207
IS - 1
SP - 75
EP - 84
AB - We show that if a Banach space X has the weak fixed point property for nonexpansive mappings and Y has the generalized Gossez-Lami Dozo property or is uniformly convex in every direction, then the direct sum X ⊕ Y with a strictly monotone norm has the weak fixed point property. The result is new even if Y is finite-dimensional.
LA - eng
KW - fixed point property; direct sum; nonexpansive mapping
UR - http://eudml.org/doc/285623
ER -