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Approximation of Fixed Points of Weak Bregman Relatively Nonexpansive Mappings in Banach Spaces

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  • Jiawei Chen
  • Zhongping Wan
  • Liuyang Yuan
  • Yue Zheng

Abstract

We introduce a concept of weak Bregman relatively nonexpansive mapping which is distinct from Bregman relatively nonexpansive mapping. By using projection techniques, we construct several modification of Mann type iterative algorithms with errors and Halpern-type iterative algorithms with errors to find fixed points of weak Bregman relatively nonexpansive mappings and Bregman relatively nonexpansive mappings in Banach spaces. The strong convergence theorems for weak Bregman relatively nonexpansive mappings and Bregman relatively nonexpansive mappings are derived under some suitable assumptions. The main results in this paper develop, extend, and improve the corresponding results of Matsushita and Takahashi (2005) and Qin and Su (2007).

Suggested Citation

  • Jiawei Chen & Zhongping Wan & Liuyang Yuan & Yue Zheng, 2011. "Approximation of Fixed Points of Weak Bregman Relatively Nonexpansive Mappings in Banach Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-23, July.
    • Handle: RePEc:hin:jijmms:420192
    DOI: 10.1155/2011/420192
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    References listed on IDEAS

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    1. Simeon Reich & Shoham Sabach, 2011. "Existence and Approximation of Fixed Points of Bregman Firmly Nonexpansive Mappings in Reflexive Banach Spaces," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 301-316, Springer.
    2. Dan Butnariu & Elena Resmerita, 2006. "Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces," Abstract and Applied Analysis, Hindawi, vol. 2006, pages 1-39, February.
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