Viscosity approximation of common fixed points of nonexpansive semigroups in Banach space
Viscosity approximation of common fixed points of nonexpansive semigroups in Banach space
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DOI：
10.1016/j.aml.2006.09.003
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发表时间：
2007-07
期刊：
影响因子：
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通讯作者：
Rudong Chen;Huimin He
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文献类型：
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作者：
Rudong Chen;Huimin He
设E是一个真实的自反Banach空间，其中存在一个从E到E的弱序列连续对偶映射，C是E的一个非空闭凸子集.设{T（t）：t≥0}是C上的非扩张半群，使得F t≥ 0 Fix（T（t）），f：C→C是固定压缩映射.当{αn}，{βn}，{tn}满足适当的条件时，得到如下两个迭代过程：强收敛于q∈ α t≥ 0 Fix（T（t）），它是以下变分不等式在F中的唯一解：我们的结果推广和改进了Suzuki [T. Suzuki，On strong convergence to common fixing points of nonexpansive semigroups in Hilbert spaces，Proc.Amer.Math.Soc.131（2002）2133-2136]和Xu [H.K.徐，Banach空间中压缩半群的一个强收敛定理，Bull. Aust。Math.Soc.72（2005）371-379]和Chen [R.陈，Banach空间中非扩张半群的公共不动点的强收敛，计算机。http：//www.sciencedirect.com/science/journal/03770427]。
Let E be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E∗, and C be a nonempty closed convex subset of E. Let {T(t):t≥0} be a nonexpansive semigroup on C such that F≔⋂t≥0Fix(T(t))≠0̸, and f:C→C be a fixed contractive mapping. When {αn},{βn},{tn} satisfy some appropriate conditions, the two iterative processes given as follows: converge strongly to q∈⋂t≥0Fix(T(t)), which is the unique solution in F to the following variational inequality: Our results extend and improve corresponding ones of Suzuki [T. Suzuki, On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces, Proc. Amer. Math. Soc. 131 (2002) 2133–2136] and Xu [H.K. Xu, A strong convergence theorem for contraction semigroups in Banach spaces, Bull. Aust. Math. Soc. 72 (2005) 371–379] and Chen [R. Chen, Strong convergence to common fixed point of nonexpansive semigroups in Banach space, Comput. Math. Appl. http://www.sciencedirect.com/science/journal/03770427].