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Weak and Strong Convergence Theorems for Zeroes of Accretive Operators in Banach Spaces

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  • Yanlai Song
  • Luchuan Ceng

Abstract

The purpose of this paper is to present two new forward‐backward splitting schemes with relaxations and errors for finding a common element of the set of solutions to the variational inclusion problem with two accretive operators and the set of fixed points of nonexpansive mappings in infinite‐dimensional Banach spaces. Under mild conditions, some weak and strong convergence theorems for approximating this common elements are proved. The methods in the paper are novel and different from those in the early and recent literature. Our results can be viewed as the improvement, supplementation, development, and extension of the corresponding results in the very recent literature.

Suggested Citation

  • Yanlai Song & Luchuan Ceng, 2014. "Weak and Strong Convergence Theorems for Zeroes of Accretive Operators in Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:943753
    DOI: 10.1155/2014/943753
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    References listed on IDEAS

    as
    1. Shuang Wang, 2012. "A Modified Regularization Method for the Proximal Point Algorithm," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, August.
    2. Shuang Wang, 2012. "A Modified Regularization Method for the Proximal Point Algorithm," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Genaro López & Victoria Martín-Márquez & Fenghui Wang & Hong-Kun Xu, 2012. "Forward‐Backward Splitting Methods for Accretive Operators in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Genaro López & Victoria Martín-Márquez & Fenghui Wang & Hong-Kun Xu, 2012. "Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-25, July.
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