Viscosity approximation methods for nonexpansive semingroups and monotone mapppings
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Let C be a nonempty closed convex subset of real Hilbert space H and F = {S(t) : t ≥ 0} a nonexpansive self-mapping semigroup of C, and f : C → C is a fixed contractive mapping. Consider the process {xn} :x_(n+1) =β_nx_n+(1−β_n)z_n z_n = α_nf(x_n) + (1 − α_n)S(t_n)P_C(x_n − r_nAx_n). It is shown that {xn} converges strongly to a common element of the set of fixed points of nonexpansive semigroups and the set of solutions of the variational inequality for an inverse strongly-monotone mapping which solves some variational inequality.
Abstract
Let C be a nonempty closed convex subset of real Hilbert space H and F = {S(t) : t ≥ 0} a nonexpansive self-mapping semigroup of C, and f : C → C is a fixed contractive mapping. Consider the process {xn} :x_(n+1) =β_nx_n+(1−β_n)z_n z_n = α_nf(x_n) + (1 − α_n)S(t_n)P_C(x_n − r_nAx_n). It is shown that {xn} converges strongly to a common element of the set of fixed points of nonexpansive semigroups and the set of solutions of the variational inequality for an inverse strongly-monotone mapping which solves some variational inequality.
참고문헌 (6)
- T. H. Kim, "Strong convergence of modi ed Mann iteration for asymptot- ically nonexpansive mappings and semigroups", Nonliear Anal, 64, pp.1140~1152 (2006)
- A. Mouda, "Viscosity approximation methods for xed points problems", J. Math. Anal. Appl, 241, pp.46~55 (2000)
- R. T. Rockafellar, "On the Maximality of Sums of Nonlinear Monotone Operators", Trans- actions of the American Mathematical Society, 149, pp.75~88 (1970)
- Y. Song, "Strong convergence theorems for nonexpansive semigroup in Banach spaces", J. Math. Anal. Appl, 318, pp.43~52 (2007)
- T. Suzuki, "Strong convergence of Krasnoselskii and Mann's type sequences for one pa- rameter nonexpansive semigroups without Bochner integrals", J. Math. Anal. Appl, 305, pp.227~239 (2005)
- H. K. Xu, "An iterative approach to quadratic optimization", J. Optim. Theory Appl, 116, pp.659~678 (2003)