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On sufficient conditions ensuring the norm convergence of an iterative sequence to zeros of accretive operators

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  • Cui, Huanhuan
  • Su, Menglong

Abstract

Given two real sequences (rn) and (αn), we study the iterative scheme: xn+1=αnu+(1-αn)Jrnxn, for finding a zero of an accretive operator A, where u is a fixed element and Jrn denotes the resolvent of A. To ensure its convergence, the real sequence (rn) is always assumed to satisfy ∑n=0∞|rn+1-rn|<∞. In this paper we show this condition can be completely removed, which enables us to improve a result recently obtained by Saejung.

Suggested Citation

  • Cui, Huanhuan & Su, Menglong, 2015. "On sufficient conditions ensuring the norm convergence of an iterative sequence to zeros of accretive operators," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 67-71.
    • Handle: RePEc:eee:apmaco:v:258:y:2015:i:c:p:67-71
    DOI: 10.1016/j.amc.2015.01.108
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    References listed on IDEAS

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    1. Fenghui Wang & Huanhuan Cui, 2012. "On the contraction-proximal point algorithms with multi-parameters," Journal of Global Optimization, Springer, vol. 54(3), pages 485-491, November.
    2. Satit Saejung, 2013. "A supplement to a regularization method for the proximal point algorithm," Journal of Global Optimization, Springer, vol. 56(1), pages 121-129, May.
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