# A note on Picard iterates of nonexpansive mappings

Annales Polonici Mathematici (2001)

- Volume: 76, Issue: 3, page 189-196
- ISSN: 0066-2216

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topEun 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 -

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