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- Title
Strong Convergence Theorems for Maximal Monotone Operators with Nonlinear Mappings in Hilbert Spaces.
- Authors
Takahashi, S.; Takahashi, W.; Toyoda, M.
- Abstract
Let C be a closed and convex subset of a real Hilbert space H. Let T be a nonexpansive mapping of C into itself, A be an α-inverse strongly-monotone mapping of C into H and let B be a maximal monotone operator on H, such that the domain of B is included in C. We introduce an iteration scheme of finding a point of F ( T)∩( A+ B)0, where F ( T) is the set of fixed points of T and ( A+ B)0 is the set of zero points of A+ B. Then, we prove a strong convergence theorem, which is different from the results of Halpern’s type. Using this result, we get a strong convergence theorem for finding a common fixed point of two nonexpansive mappings in a Hilbert space. Further, we consider the problem for finding a common element of the set of solutions of a mathematical model related to equilibrium problems and the set of fixed points of a nonexpansive mapping.
- Subjects
HILBERT space; NONEXPANSIVE mappings; MONOTONE operators; MATHEMATICAL models; ITERATIVE methods (Mathematics)
- Publication
Journal of Optimization Theory & Applications, 2010, Vol 147, Issue 1, p27
- ISSN
0022-3239
- Publication type
Article
- DOI
10.1007/s10957-010-9713-2