URN 
etd0516111182003 
Author 
Peilin Lai 
Author's Email Address 
No Public. 
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Department 
Applied Mathematics 
Year 
2010 
Semester 
2 
Degree 
Master 
Type of Document 

Language 
English 
Title 
Iterative Methods for Common Fixed Points of Nonexpansive Mappings in Hilbert spaces 
Date of Defense 
20100617 
Page Count 
29 
Keyword 
Nonexpansive mapping
Convex optimization
Contraction
Fixed point
Viscosity approximation

Abstract 
The aim of this work is to propose viscositylike methods for finding a specific common fixed point of a finite family T={ T_{i} }_{i=1}^{N} of nonexpansive selfmappings of a closed convex subset C of a Hilbert space H.We propose two schemes: one implicit and the other explicit.The implicit scheme determines a set {x_{t} : 0 < t < 1} through the fixed point equation x_{t}= tf (x_{t} ) + (1− t)Tx_{t}, where f : C→C is a contraction.The explicit scheme is the discretization of the implicit scheme and de defines a sequence {x_{n} } by the recursion x_{n+1}=α\_{n}f(x_{n}) +(1−α\_{n})Tx_{n} for n ≥ 0, where {α\_{n} }⊂ (0,1) It has been shown in the literature that both implicit and explicit schemes converge in norm to a fixed point of T (with additional conditions imposed on the sequence {α _{n} } in the explicit scheme).We will extend both schemes to the case of a finite family of nonexpansive mappings. Our proposed schemes converge in norm to a common fixed point of the family which in addition solves a variational inequality. 
Advisory Committee 
LaiJiu Lin  chair
JenChih Yao  cochair
NgaiChing Wong  cochair
HongKun Xu  advisor

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indicate access worldwide 
Date of Submission 
20110516 