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

^*Corresponding author for this work

Department of Mathematics

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

22 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	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 Lipschitzian mapping
Uniformly convex metric space

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2012.08.013

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@article{31a712aabdd94120a3ad40c1bf92de17,

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 Lipschitzian mapping, Uniformly convex metric space",

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

year = "2013",

month = jan,

day = "15",

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

language = "English",

volume = "397",

pages = "861--868",

journal = "Journal of Mathematical Analysis and Applications",

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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 Lipschitzian mapping

KW - Uniformly convex metric space

UR - https://www.scopus.com/pages/publications/84867139770

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

Abstract

Keywords

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