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:10.1155/2010/547828Published: 5 January 2011
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 .