Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces
Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces
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DOI：
10.1016/j.jmaa.2006.08.036
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发表时间：
2007-07-01
影响因子：
1.3
通讯作者：
Takahashi, Wataru
中科院分区：
文献类型：
--
作者：
Takahashi, Satoru;Takahashi, Wataru
本文用黏度近似法给出了求Hilbert空间中平衡问题解集和非扩张映射不动点集的公共元素的迭代格式。然后，我们证明了一个与Combettes和Hirstoaga的结果相联系的强收敛定理[PL. Combettes， S.A. Hirstoaga， Hilbert空间的平衡规划，J.非线性凸分析，6(2005)116 -136]和Wittmann的结果[R.]维特曼，非扩张映射不动点的逼近，Arch。数学，58(1992)486-491。利用这一结果，我们得到了两个改进和推广原有结果的推论。(C) 2006爱思唯尔公司版权所有。
In this paper, we introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Then, we prove a strong convergence theorem which is connected with Combettes and Hirstoaga's result [PL. Combettes, S.A. Hirstoaga, Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal. 6 (2005) 117-136] and Wittmann's result [R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992) 486-491]. Using this result, we obtain two corollaries which improve and extend their results. (C) 2006 Elsevier Inc. All rights reserved.