Acta mathematica scientia,Series A ›› 2004, Vol. 4 ›› Issue (6): 730-736.

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Iterative Processes with Errors for Fixed Points \=of Nonlinear |ΦPseudocontractive Mappings

 XU Yu-Guang   

  • Online:2004-12-25 Published:2004-12-25
  • Supported by:

    本项工作由国家自然科学基金(19961004)和云南省自然科学基金资助

Abstract:

The purpose of this paper is to introduce Φpseudocontractive mappings-aclass of mappings which is much more general than the important class of strongly pseudocontractive mappings and to study approximate problems of fixed point for the mappings by Ishikawa and Mann iterative processes with errors in  more general settings. The results presented in this paper show that the uniformly continuity of mapping T ensures the Ishikawa iterative sequence converges strongly to unique fixed point of T in a Banach space X; if X is uniformly smooth then the continuity of T is not necessary.

Key words: Φpseudocontractive mapping, strongly pseudocontractive mapping, Mann iteration sequence, Ishikawa iteration sequence

CLC Number: 

  • 47H09
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