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The general iterative methods for nonexpansive mappings in Banach spaces

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Abstract

In this paper, we introduce a general iterative approximation method for finding a common fixed point of a countable family of nonexpansive mappings which is a unique solution of some variational inequality. We prove the strong convergence theorems of such iterative scheme in a reflexive Banach space which admits a weakly continuous duality mapping. As applications, at the end of the paper, we apply our results to the problem of finding a zero of an accretive operator. The main result extends various results existing in the current literature.

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Correspondence to Rabian Wangkeeree.

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Supported by The Thailand Research Fund, Grant TRG5280011.

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Wangkeeree, R., Petrot, N. & Wangkeeree, R. The general iterative methods for nonexpansive mappings in Banach spaces. J Glob Optim 51, 27–46 (2011). https://doi.org/10.1007/s10898-010-9617-6

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  • DOI: https://doi.org/10.1007/s10898-010-9617-6

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