Mann iteration process for asymptotic pointwise nonexpansive mappings in metric spaces

B. A. Ibn Dehaish; M. A. Khamsi; A. R. Khan

doi:10.1016/j.jmaa.2012.08.013

Mann iteration process for asymptotic pointwise nonexpansive mappings in metric spaces

B. A. Ibn Dehaish, M. A. Khamsi, A. R. Khan

Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

Let (M, d) be a complete 2-uniformly convex metric space. Let C be a nonempty, bounded, closed, and convex subset of M, and let T:. C→ C be an asymptotic pointwise nonexpansive mapping. In this paper, we prove that the modified Mann iteration process defined by x _n+1=t _nT ⁿ(x _n)⊕(1-t _n)x _n converges in a weaker sense to a fixed point of T.

Original language	British English
Pages (from-to)	861-868
Number of pages	8
Journal	Journal of Mathematical Analysis and Applications
Volume	397
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2012.08.013
State	Published - 15 Jan 2013

Keywords

Asymptotic pointwise nonexpansive mapping
Asymptotically nonexpansive mapping
Fixed point
Inequality of Bruhat and Tits
Mann iteration process
Uniformly convex metric space
Uniformly Lipschitzian mapping

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10.1016/j.jmaa.2012.08.013

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title = "Mann iteration process for asymptotic pointwise nonexpansive mappings in metric spaces",

abstract = "Let (M, d) be a complete 2-uniformly convex metric space. Let C be a nonempty, bounded, closed, and convex subset of M, and let T:. C→ C be an asymptotic pointwise nonexpansive mapping. In this paper, we prove that the modified Mann iteration process defined by x n+1=t nT n(x n)⊕(1-t n)x n converges in a weaker sense to a fixed point of T.",

keywords = "Asymptotic pointwise nonexpansive mapping, Asymptotically nonexpansive mapping, Fixed point, Inequality of Bruhat and Tits, Mann iteration process, Uniformly convex metric space, Uniformly Lipschitzian mapping",

author = "{Ibn Dehaish}, {B. A.} and Khamsi, {M. A.} and Khan, {A. R.}",

year = "2013",

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doi = "10.1016/j.jmaa.2012.08.013",

language = "British English",

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T1 - Mann iteration process for asymptotic pointwise nonexpansive mappings in metric spaces

AU - Ibn Dehaish, B. A.

AU - Khamsi, M. A.

AU - Khan, A. R.

PY - 2013/1/15

Y1 - 2013/1/15

N2 - Let (M, d) be a complete 2-uniformly convex metric space. Let C be a nonempty, bounded, closed, and convex subset of M, and let T:. C→ C be an asymptotic pointwise nonexpansive mapping. In this paper, we prove that the modified Mann iteration process defined by x n+1=t nT n(x n)⊕(1-t n)x n converges in a weaker sense to a fixed point of T.

AB - Let (M, d) be a complete 2-uniformly convex metric space. Let C be a nonempty, bounded, closed, and convex subset of M, and let T:. C→ C be an asymptotic pointwise nonexpansive mapping. In this paper, we prove that the modified Mann iteration process defined by x n+1=t nT n(x n)⊕(1-t n)x n converges in a weaker sense to a fixed point of T.

KW - Asymptotic pointwise nonexpansive mapping

KW - Asymptotically nonexpansive mapping

KW - Fixed point

KW - Inequality of Bruhat and Tits

KW - Mann iteration process

KW - Uniformly convex metric space

KW - Uniformly Lipschitzian mapping

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U2 - 10.1016/j.jmaa.2012.08.013

DO - 10.1016/j.jmaa.2012.08.013

M3 - Article

AN - SCOPUS:84867139770

SN - 0022-247X

VL - 397

SP - 861

EP - 868

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Mann iteration process for asymptotic pointwise nonexpansive mappings in metric spaces

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