Implicit Iterative Scheme for a Countable Family of Nonexpansive Mappings in 2‐Uniformly Smooth Banach Spaces

Ming Tian and Xin Jin

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: Implicit Mann process and Halpern‐type iteration have been extensively studied by many others. In this paper, in order to find a common fixed point of a countable family of nonexpansive mappings in the framework of Banach spaces, we propose a new implicit iterative algorithm related to a strongly accretive and Lipschitzian continuous operator F : xn = αnγV(xn) + βnxn−1 + ((1 − βn)I − αnμF)Tnxn and get strong convergence under some mild assumptions. Our results improve and extend the corresponding conclusions announced by many others.

Date: 2013
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https://doi.org/10.1155/2013/264910

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:264910

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