New Iterative Approximation Methods for a Countable Family of Nonexpansive Mappings in Banach Spaces | Zendy

Kamonrat Nammanee | Zendy; Rabian Wangkeeree | Zendy

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New Iterative Approximation Methods for a Countable Family of Nonexpansive Mappings in Banach Spaces

Author(s) -

Kamonrat Nammanee,

Rabian Wangkeeree

Publication year - 2010

Publication title -

fixed point theory and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.826

H-Index - 63

eISSN - 1687-1820

pISSN - 1687-1812

DOI - 10.1155/2011/671754

Subject(s) - mathematics , banach space , countable set , differential geometry , convergence (economics) , fixed point , uniformly convex space , duality (order theory) , pure mathematics , zero (linguistics) , discrete mathematics , banach manifold , mathematical analysis , lp space , linguistics , philosophy , economics , economic growth

We introduce new general iterative approximation methods for finding a common fixed point of a countable family of nonexpansive mappings. Strong convergence theorems are established in the framework of reflexive Banach spaces which admit a weakly continuous duality mapping. Finally, we apply our results to solve the the equilibrium problems and the problem of finding a zero of an accretive operator. The results presented in this paper mainly improve on the corresponding results reported by many others.

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