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Convergence Analysis for Inertial Krasnoselskii-Mann Type Iterative Algorithms

We consider the problem of finding a common fixed point of an infinite family ${T_n}$
of nonlinear self-mappings of a closed convex subset $C$ of a real Hilbert space $H$. Namely,
we want to find a point $x$ with the property (assuming such common fixed points exist):
[
xin igcap_{n=1}^infty ext{Fix}(T_n).
]
We will use the Krasnoselskii-Mann (KM) Type inertial iterative algorithms of the form
$$ x_{n+1} = ((1-alpha_n)I+alpha_nT_n)y_n,quad
y_n = x_n + eta_n(x_n-x_{n-1}).eqno(*)$$
We discuss the convergence properties of the sequence ${x_n}$ generated by this algorithm (*).
In particular, we prove that ${x_n}$ converges weakly to a common fixed point of the family
${T_n}$ under certain conditions imposed on the sequences ${alpha_n}$ and ${eta_n}$.

Identiferoai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0216111-213732
Date16 February 2011
CreatorsHuang, Wei-Shiou
ContributorsLai-Jiu Lin, Hong-Kun Xu, Jen-Chih Yao, Ngai-Ching Wong
PublisherNSYSU
Source SetsNSYSU Electronic Thesis and Dissertation Archive
LanguageEnglish
Detected LanguageEnglish
Typetext
Formatapplication/pdf
Sourcehttp://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0216111-213732
Rightsunrestricted, Copyright information available at source archive

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