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关于广义Φ-压缩映射几种迭代序列收敛的等价性

The Equivalence of Iterative Sequences Convergence for a Class Nonlinear Mapping
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摘要 在广义Φ-压缩映射条件下,分别得到了Picard迭代序列与Krasnoselskii迭代序列以及Mann迭代序列与Ishikawa迭代序列收敛的等价性. In this paper, it is shown that the convergence of Noor iteration sequence is equivalent to Mann iteration sequence, and the convergence of Mann iteration sequence is equivalent to Ishikawa iteration sequence for generalized φ- contractive mappings in an arbitrary real Banach spaces.
作者 张健 翟全礼
出处 《数学的实践与认识》 CSCD 北大核心 2011年第12期243-248,共6页 Mathematics in Practice and Theory
关键词 广义φ-压缩映射 不动点 Picard迭代序列 MANN迭代序列 Ishikawa迭 代序列 generalized φ- contractive mappings fixed point Noor iteration sequence Mann iteration sequence Ishikawa iteration sequence
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参考文献6

  • 1Deimling K. Zeros of accretive operators[J]. Manuscripta Math, 1974, 13: 365-374.
  • 2Mann W R. Mean value methods in iteration[J]. Proc. Amer. Math. Soc, 1953, 4: 506-510.
  • 3Ishikawa S. Fixed points by a new iteration method[J]. Proc. Amer. Math. Soc, 44, 1974; 147-150.
  • 4Zamfirescu T. Fixed point theorems in metric[J]. Archiv der Mathamatik, 1972, 23: 292-298.
  • 5Soltuz S M. The equivalence of Picard, Mann and Ishikawa iterations dealing with quasi-contractive operators[J]. Math. Comm, 2005, 10: 81-88.
  • 6Xue Zhiqun, Remarks of equivalence among Picard, Mann and ishikawa iteration in normed spaces[J]. Fixed Point Theory and Applications, Volume 2007, Article ID 61434, 5.

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