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Approximation of Nearest Common Fixed Point of Nonexpansive Mappings in Hilbert Spaces

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Abstract

The purpose of this paper is to study the convergence problem of the iteration scheme x n+1 = λ n+1y +(1–λ n+1) T n+1 x n for a family of infinitely many nonexpansive mappings T 1, T 2, . . . in a Hilbert space. It is proved that under suitable conditions this iteration scheme converges strongly to the nearest common fixed point of this family of nonexpansive mappings. The results presented in this paper extend and improve some recent results.

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Authors and Affiliations

  1. Department of Mathematics, Yibin University, Yibin 644007, P. R. China

    Shi Sheng Zhang

  2. Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China

    Shi Sheng Zhang

  3. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, P. R. China

    H. W. Joseph Lee & Chi Kin Chan

Authors
  1. Shi Sheng Zhang
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  2. H. W. Joseph Lee
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  3. Chi Kin Chan
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Correspondence to Shi Sheng Zhang.

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Supported by The Research Foundation Grant of The Hong Kong Polytechnic University and Yibin University (2005Z3)

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Zhang, S.S., Joseph Lee, H.W. & Chan, C.K. Approximation of Nearest Common Fixed Point of Nonexpansive Mappings in Hilbert Spaces. Acta Math Sinica 23, 1889–1896 (2007). https://doi.org/10.1007/s10114-005-0821-0

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  • DOI: https://doi.org/10.1007/s10114-005-0821-0

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