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实Banach空间中渐近半压缩映射的强收敛性     被引量:2

Strong convergence for asymptotically demicontractive mappings in real Banach space.

文献类型:期刊文献

中文题名:实Banach空间中渐近半压缩映射的强收敛性

英文题名:Strong convergence for asymptotically demicontractive mappings in real Banach space.

作者:倪仁兴[1]

机构:[1]绍兴文理学院数学系

年份:2006

卷号:33

期号:1

起止页码:7

中文期刊名:浙江大学学报:理学版

收录:CSTPCD、、北大核心2004、Scopus、CSCD2011_2012、北大核心、CSCD

基金:国家自然科学基金资助项目(10271025);浙江省自然科学基金资助项目(102002)

语种:中文

中文关键词:渐近半压缩映射;k-严格渐近伪压缩映象;q-一致光滑实Banach空间;任意实Banach空间;一致L-Lipschitzian映射

外文关键词:asymptotically demicontractive mappings; k-strictly asymptotically pscudocontractive mappings; q-unifromaly smooth real Banach speces; arbitrary real Banach spaces; uniformly L-Lipschitzian mappings

中文摘要:利用新的分析技巧,建立了任意实Banach空间中具随机误差的Ishikawa迭代法生成的序列{xn}强收敛于渐近半压缩映射的不动点的一些充要条件.作为应用,证明了Oslike和Aniagbosor最近的q-一致光滑实Banach空间中渐近半压缩映射的不动点的迭代逼近的一主要结果(它本身主要是1998年Osilike的一定理的一般化)能被延拓至任意实Banach空间上,并给出了Ishikawa迭代序列的误差估计,且所用证明方法比已有的简单.

外文摘要:By using a new analysis technique, some sufficient and necessary conditions on strong convergence of sequence{xn }generated from the Ishikawa iteration method with random errors to fixed points of asymptotically demicontractive mappings are established in arbitrary real Banach spaces. As application, it is proved that a recent main result of Oslike and Aniagbosor (Which is itself a generalization of a theorem of Osilike(1998) ) concerning the iterarive approximation of fixed points of asymptotically demicontractive mappings in q-unifomly smooth real Banach space( 1〈q〈+∞)can be extended to arbitrary real Banach spaces. Error estimate of Ishikawa iterative sequence is given. Furthermore, the methods of proofs are quite different and simple.

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