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 ${eta_n}$.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0216111-213732 |
| Date | 16 February 2011 |
| Creators | Huang, Wei-Shiou |
| Contributors | Lai-Jiu Lin, Hong-Kun Xu, Jen-Chih Yao, Ngai-Ching Wong |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0216111-213732 |
| Rights | unrestricted, Copyright information available at source archive |
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