一致L-Lipschitz的渐近拟伪压缩型映象迭代收敛的充要条件

向长合

系统科学与数学 ›› 2008, Vol. 28 ›› Issue (4) : 447-455.

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系统科学与数学 ›› 2008, Vol. 28 ›› Issue (4) : 447-455. DOI: 10.12341/jssms10096
论文

一致L-Lipschitz的渐近拟伪压缩型映象迭代收敛的充要条件

    向长合
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A Necessary and Sufficient Condition for the Iterative Sequence Convergence to the Fixed Point of Uniformly L-Lipschitz Asymptotically Quasi Pseudo-Contractive Type Mapping

    XIANG Changhe
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摘要

设E是任意的实Banach空间,C是E的非空凸子集(C可以是E的无界子集), T:C→C是一致L-Lipschitz的渐近拟伪压缩型映象, 在对参数的一些限制条件下,该文给出了带误差的修改的Ishikawa迭代序列强收敛于T的不动点的充要条件.

Abstract

Suppose E is a real Banach space, Cis a nonempty convex subset of E(C may be a unbounded subset ofE), T:C→C is a uniformly L-Lipschitzian asymptotically quasi pseudo-contractive type mapping, under some restrictive conditions on the parameters, a
necessary and sufficient condition is given for the modified Ishikawa iterative sequence with error to converge strongly to a fixed point of T.

关键词

渐近拟伪压缩型映象 / 带误差的修改的Ishikawa迭代序列 / 不动点.

Key words

Asymptotically quasi pseudo-contractive type mapping / modified Ishikawa iterative sequence with error / fixed points.

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向长合. 一致L-Lipschitz的渐近拟伪压缩型映象迭代收敛的充要条件. 系统科学与数学, 2008, 28(4): 447-455. https://doi.org/10.12341/jssms10096
XIANG Changhe. A Necessary and Sufficient Condition for the Iterative Sequence Convergence to the Fixed Point of Uniformly L-Lipschitz Asymptotically Quasi Pseudo-Contractive Type Mapping. Journal of Systems Science and Mathematical Sciences, 2008, 28(4): 447-455 https://doi.org/10.12341/jssms10096
中图分类号： 47H09    47H10   
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