Research Article
Convergence of Paths for Perturbed Maximal Monotone Mappings in Hilbert Spaces
1 Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China
2 Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China
3 Department of Mathematics, Gyeongsang National University, Jinju 660-701, Republic of Korea
Fixed Point Theory and Applications 2010, 2010:547828 doi:10.1155/2010/547828
Published: 5 January 2011Abstract
Let 
be a Hilbert space and 
a nonempty closed convex subset of 
. Let 
be a maximal monotone mapping and 
a bounded demicontinuous strong pseudocontraction. Let 
be the unique solution to the equation 
. Then
is bounded if and only if 
converges strongly to a zero point of A as 
which is the unique solution in 
, where 
denotes the zero set of 
, to the following variational inequality 
, for all 
.
