Taiwanese Journal of Mathematics

WEAK AND STRONG CONVERGENCE FOR SOME OF NONEXPANSIVE MAPPINGS

Alireza Medghalchi and Shahram Saeidi

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Abstract

IIn this paper, we deal with a class of nonexpansive mappings with the property $D(\overline{co} F_{\frac 1n} (T),F(T))\to 0$, as $n\to \infty$, where $D$ is the Hausdorff metric. We show that nonexpansive mappings with compact domains enjoy this property and give some examples of this kind of mappings with noncompact domains in $l^\infty$. Then we prove a nonlinear ergodic theorem, and a convergence theorem of mann's type for this kind of mappings.

Article information

Source
Taiwanese J. Math., Volume 12, Number 9 (2008), 2489-2499.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405191

Digital Object Identifier
doi:10.11650/twjm/1500405191

Mathematical Reviews number (MathSciNet)
MR2479067

Zentralblatt MATH identifier
1220.47105

Subjects
Primary: 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]

Keywords
fixed point nonexpansive mapping nonlinear ergodic theorem mapping of type ($\gamma$) strong convergence mann's type

Citation

Medghalchi, Alireza; Saeidi, Shahram. WEAK AND STRONG CONVERGENCE FOR SOME OF NONEXPANSIVE MAPPINGS. Taiwanese J. Math. 12 (2008), no. 9, 2489--2499. doi:10.11650/twjm/1500405191. https://projecteuclid.org/euclid.twjm/1500405191


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References

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