URN 
etd0216111213732 
Author 
WeiShiou Huang 
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 
Convergence Analysis for Inertial KrasnoselskiiMann Type Iterative Algorithms 
Date of Defense 
20100617 
Page Count 
32 
Keyword 
demiclosedness principle
KM Type iterative algorithms
inertial iteration
fixed point
Weak convergence
nonexpansive mapping

Abstract 
We consider the problem of finding a common fixed point of an infinite family ${T_n}$ of nonlinear selfmappings 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 KrasnoselskiiMann (KM) Type inertial iterative algorithms of the form $$ x_{n+1} = ((1alpha_n)I+alpha_nT_n)y_n,quad y_n = x_n + eta_n(x_nx_{n1}).eqno(*)$$ 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 ${eta_n}$. 
Advisory Committee 
LaiJiu Lin  chair
JenChih Yao  cochair
NgaiChing Wong  cochair
HongKun Xu  advisor

Files 
indicate access worldwide 
Date of Submission 
20110216 