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The split common xed point problem has been investigated recently,<br> which is a generalization of the split feasibility problem and of the convex feasibility<br> problem. We construct a cyclic algorithm to approximate a solution of the split<br> common xed point problem for the demicontractive mappings in a Hilbert space.<br> Our results improve and extend previously discussed related problems and algorithms
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This article was downloaded by: [Xi'an Jiaotong University]
On: 14 January 2013, At: 18:22
Publisher: Taylor & Francis
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Mathematical Modelling and
Analysis
Publication details, including instructions for authors and
subscription information:
http://www.tandfonline.com/loi/tmma20
A Cyclic Algorithm for the Split
Common Fixed Point Problem
of Demicontractive Mappings in
Hilbert Spaces
Yu-Chao Tang
a
b
, Ji-Gen Peng
b
& Li-Wei Liu
a
a
NanChang University, 330031, Nanchang, China
b
Xi'an Jiaotong University, 710049, Xi'an, China
Version of record first published: 24 Aug 2012.
To cite this article: Yu-Chao Tang , Ji-Gen Peng & Li-Wei Liu (2012): A Cyclic Algorithm
for the Split Common Fixed Point Problem of Demicontractive Mappings in Hilbert Spaces,
Mathematical Modelling and Analysis, 17:4, 457-466
To link to this article: http://dx.doi.org/10.3846/13926292.2012.706236
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Mathematical Modelling and Analysis Publisher: Taylor&Francis and VGTU
Volume 17 Number 4, September 2012, 457–466 http://www.tandfonline.com/TMMA
http://dx.doi.org/10.3846/13926292.2012.706236 Print ISSN: 1392-6292
c
Vilnius Gediminas Technical University, 2012 Online ISSN: 1648-3510
A Cyclic Algorithm for the Split Common
Fixed Point Problem of Demicontractive
Mappings in Hilbert Spaces
∗
Yu-Chao Tang
a,b
, Ji-Gen Peng
b
and Li-Wei Liu
a
a
NanChang University
330031 Nanchang, China
b
Xi’an Jiaotong University
710049 Xi’an, China
E-mail: hhaaoo1331@yahoo.com.cn
Received June 27, 2011; revised April 27, 2012; published online September 1, 2012
Abstract. The split common fixed point problem has been investigated recently,
which is a generalization of the split feasibility problem and of the convex feasibility
problem. We construct a cyclic algorithm to approximate a solution of the split
common fixed point problem for the demicontractive mappings in a Hilbert space.
Our results improve and extend previously discussed related problems and algorithms.
Keywords: split feasibility problem, demicontractive mappings, common fixed point.
AMS Subject Classification: 49J53; 65K10.
1 Introduction
Let H be a real Hilbert space with inner product h·,·i and norm k·k, respectively.
Recall that the convex feasibility problem (CFP) is formulated as follows: If
T
n
i=1
C
i
6= ∅,
Find a point x
∗
∈
n
\
i=1
C
i
, (1.1)
where n ≥ 1 is an integer, and each C
i
is a nonempty closed convex subset of
H. It has been proved that the convex feasibility problem has great applicabil-
ity in many areas, such as image reconstruction in computerized tomography,
∗
This work was supported by the National Natural Science Foundations of China (11131006,
60970149, 11101204, 11102078), the Natural Science Foundations of Jiangxi Province
(2009GZS0021, CA201107114) and the Youth Science Funds of The Education Depart-
ment of Jiangxi Province (GJJ12141).
Downloaded by [Xi'an Jiaotong University] at 18:22 14 January 2013
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