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2008•Journal of Sichuan Normal UniversityRequires access

The Convergence for Asymptotically Nonexpansive Mappings in Banach Spaces

MA Li-rong

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Abstract

In this paper,we first introduce some iterative processes for asymptotically nonexpansive mappings in Banach spaces and then discuss the strong convergence for the iterative processes.By using Banach compression image principle and applying iterative scheme with errors and inequality technique,the necessary and sufficient conditions for the strong convergence of the iterative sequence of asymptotically nonexpansive mappings in Banach spaces are obtained.The results presented in this paper extend and improve some recent results in literature.

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What this paper is about

In this paper,we first introduce some iterative processes for asymptotically nonexpansive mappings in Banach spaces and then discuss the strong convergence for the iterative processes.By using Banach compression image principle and applying iterative scheme with errors and inequality technique,the necessary and sufficient conditions for the strong convergence of the iterative sequence of asymptotically nonexpansive mappings in Banach spaces are obtained.The results presented in this paper extend and improve some recent results in literature.

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Available abstract

In this paper,we first introduce some iterative processes for asymptotically nonexpansive mappings in Banach spaces and then discuss the strong convergence for the iterative processes.By using Banach compression image principle and applying iterative scheme with errors and inequality technique,the necessary and sufficient conditions for the strong convergence of the iterative sequence of asymptotically nonexpansive mappings in Banach spaces are obtained.The results presented in this paper extend and improve some recent results in literature.

Key concepts: Banach space, Mathematics, Convergence (economics), Sequence (biology), Fixed point, Scheme (mathematics), Iterative method, Applied mathematics

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