Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals
Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals
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DOI：
10.1016/j.jmaa.2004.11.017
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发表时间：
2005-05-01
影响因子：
1.3
通讯作者：
Suzuki, T
中科院分区：
文献类型：
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作者：
Suzuki, T
本文在不使用Bochner积分和不假设Banach空间严格凸性的情况下，证明了非扩张半群的Krasnoselskii和Mann型收敛定理.我们的主要结果之一是：设C是Banach空间E的紧凸子集，{T（t）：t >= 0}是C上的单指标强连续非扩张映射半群.设{t（n）}是[0，infinity）中满足[GRAPHICS]的序列设lambda是（0，1）中的元素。在C中定义一个序列{x（n）}，其中x（1）是C的一个元素，x（n+1）= lambda T（t（n））x（n）+（1-lambda）x（n），n是N的一个元素.则{x（n）}强收敛于{T（t）：t >= 0}的公共不动点。(c)2004年爱思唯尔公司All rights reserved.
In this paper, we prove Krasnoselskii and Mann's type convergence theorems for nonexpansive semigroups without using Bochner integral and without assuming the strict convexity of Banach spaces. One of our main results is the following: let C be a compact convex subset of a Banach space E and let {T(t): t >= 0} be a one-parameter strongly continuous semigroup of nonexpansive mappings on C. Let {t(n)} be a sequence in [0, infinity) satisfying[GRAPHICS]Let lambda is an element of (0, 1). Define a sequence {x(n)} in C by x(1) is an element of C andx(n+1) = lambda T(t(n))x(n) + (1-lambda)x(n)for n is an element of N. Then {x(n)} converges strongly to a common fixed point of {T(t): t >= 0}. (c) 2004 Elsevier Inc. All rights reserved.