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

Jiawei Chen | Zendy; Zhongping Wan | Zendy; L. C. L. Yuan | Zendy; Yue Zheng | Zendy

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

Author(s) -

Jiawei Chen,

Zhongping Wan,

L. C. L. Yuan,

Yue Zheng

Publication year - 2011

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2011/420192

Subject(s) - bregman divergence , mathematics , banach space , fixed point , convergence (economics) , projection (relational algebra) , type (biology) , iterative method , pure mathematics , mathematical analysis , mathematical optimization , algorithm , ecology , economics , biology , economic growth

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)

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