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Keywords
(7)
Fixed Point
Hilbert Space
Iteration Method
Iterative Algorithm
Monotone Operator
nonexpansive mapping
Variational Inequality
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A general iterative algorithm for nonexpansive mappings in Hilbert spaces
A general iterative algorithm for nonexpansive mappings in Hilbert spaces,10.1016/j.na.2010.03.058,Nonlinear Analysistheory Methods & Applications,Mi
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A general iterative algorithm for nonexpansive mappings in Hilbert spaces
(
Citations: 7
)
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Ming Tian
Let H be a real Hilbert space. Suppose that T is a
nonexpansive mapping
on H with a fixed point, f is a contraction on H with coefficient 0α1, and F:H→H is a kLipschitzian and ηstrongly
monotone operator
with k>0,η>0. Let 0μ2η/k2,0γμ(η−μk22)/α=τ/α. We proved that the sequence {xn} generated by the iterative method xn+1=αnγf(xn)+(I−μαnF)Txn converges strongly to a
fixed point
x̃∈Fix(T), which solves the
variational inequality
〈(γf−μF)x̃,x−x̃〉≤0, for x∈Fix(T).
Journal:
Nonlinear Analysistheory Methods & Applications  NONLINEAR ANALTHEOR METH APP
, vol. 73, no. 3, pp. 689694, 2010
DOI:
10.1016/j.na.2010.03.058
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Citation Context
(1)
...Very recently,M.Tian [
9
] proposed a general iterative method for Nonexpansive Mappings that contains algorithms defined by G.Marino,H.K.Xu and Yamada :...
...where T is a selfnonexpansive mapping on H,F is k−Lipschitzian continuous and η−strongly monotone operator on H and f is a contraction on H.Then M.Tian[
9
] proved the sequence defined by above iterative process converges strongly to a fixed point of T...
...Then we extend and generalize the iterative method introduced by Tian [
9
] and consider the following general iterative method...
Ming Tian
.
A General Iterative Method Based on the Hybrid Steepest Descent Scheme...
References
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Journal:
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Minimizing certain convex functions over the intersection of the fixed point sets of nonexpansive mappings
(
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,
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A general iterative method for nonexpansive mappings in Hilbert spaces
(
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Giuseppe Marino
,
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Journal:
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(
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Xiaolong Qin
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,
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Journal:
Nonlinear Analysistheory Methods & Applications  NONLINEAR ANALTHEOR METH APP
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ITERATIVE ALGORITHMS FOR NONLINEAR OPERATORS
(
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Journal:
Journal of The London Mathematical Societysecond Series  J LONDON MATH SOCSECOND SER
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Citations
(7)
A general composite iterative algorithm for nonexpansive mappings in Hilbert spaces
LuChuan Ceng
,
SyMing Guu
,
JenChih Yao
Journal:
Computers & Mathematics With Applications  COMPUT MATH APPL
, vol. 61, no. 9, pp. 24472455, 2011
A note on the hybrid steepest descent methods
Koji Aoyama
,
Yasunori Kimura
Published in 2011.
A general iterative method for obtaining an infinite family of strictly pseudocontractive mappings in Hilbert spaces
Shuang Wang
Journal:
Applied Mathematics Letters
, vol. 24, no. 6, pp. 901907, 2011
A Solution of variational inequality problem for a finite family of nonexpansive mappings in Hilbert spaces
Farrukh Mukhamedov
,
Mansoor Saburov
Published in 2010.
Solution of variational inequality problems on fixed point sets of nonexpansive mappings using iterative methods
Eric U. Ofoedu
Published in 2010.