Title page for etd-0516111-182003


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URN etd-0516111-182003
Author Pei-lin 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 2010-06-17
Page Count 29
Keyword
  • Nonexpansive mapping
  • Convex optimization
  • Contraction
  • Fixed point
  • Viscosity approximation
  • Abstract The aim of this work is to propose viscosity-like methods for finding a specific common fixed point of a finite family T={ T_{i} }_{i=1}^{N} of nonexpansive self-mappings 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
  • Lai-Jiu Lin - chair
  • Jen-Chih Yao - co-chair
  • Ngai-Ching Wong - co-chair
  • Hong-Kun Xu - advisor
  • Files
  • etd-0516111-182003.pdf
  • indicate access worldwide
    Date of Submission 2011-05-16

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