Convergence of Paths for Perturbed Maximal Monotone Mappings in Hilbert Spaces
Qing Yuan, Xiaolong Qin, Haiyun Zhou, Shin-Min Kang · Fixed Point Theory and Applications · 2011
Abstract Let "Equation missing" be a Hilbert space and "Equation missing" a nonempty closed convex subset of "Equation missing". Let "Equation missing" be a maximal monotone mapping and "Equation missing" a bounded demicontinuous strong pseudocontraction. Let "Equation missing" be the unique solution to the equation "Equation missing". Then"Equation missing" is bounded if and only if "Equation missing" converges strongly to a zero point of A as "Equation missing" which is the unique solution in "Equation missing", where "Equation missing" denotes the zero set of "Equation missing", to the following variational inequality "Equation missing", for all "Equation missing".