A note on Picard iterates of nonexpansive mappings

Eun Suk Kim, and W. A. Kirk. "A note on Picard iterates of nonexpansive mappings." Annales Polonici Mathematici 76.3 (2001): 189-196. <http://eudml.org/doc/280360>.

@article{EunSukKim2001,
abstract = {Let X be a Banach space, C a closed subset of X, and T:C → C a nonexpansive mapping. It has recently been shown that if X is reflexive and locally uniformly convex and if the fixed point set F(T) of T has nonempty interior then the Picard iterates of the mapping T always converge to a point of F(T). In this paper it is shown that if T is assumed to be asymptotically regular, this condition can be weakened much further. Finally, some observations are made about the geometric conditions imposed.},
author = {Eun Suk Kim, W. A. Kirk},
journal = {Annales Polonici Mathematici},
keywords = {fixed points; nonexpansive mappings; Picard iterates},
language = {eng},
number = {3},
pages = {189-196},
title = {A note on Picard iterates of nonexpansive mappings},
url = {http://eudml.org/doc/280360},
volume = {76},
year = {2001},
}

TY - JOUR
AU - Eun Suk Kim
AU - W. A. Kirk
TI - A note on Picard iterates of nonexpansive mappings
JO - Annales Polonici Mathematici
PY - 2001
VL - 76
IS - 3
SP - 189
EP - 196
AB - Let X be a Banach space, C a closed subset of X, and T:C → C a nonexpansive mapping. It has recently been shown that if X is reflexive and locally uniformly convex and if the fixed point set F(T) of T has nonempty interior then the Picard iterates of the mapping T always converge to a point of F(T). In this paper it is shown that if T is assumed to be asymptotically regular, this condition can be weakened much further. Finally, some observations are made about the geometric conditions imposed.
LA - eng
KW - fixed points; nonexpansive mappings; Picard iterates
UR - http://eudml.org/doc/280360
ER -