Weak and strong convergence theorems of implicit iteration process on Banach spacesReport as inadecuate




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Fixed Point Theory and Applications

, 2011:96

First Online: 06 December 2011Received: 19 August 2011Accepted: 06 December 2011

Abstract

In this article, we first consider weak convergence theorems of implicit iterative processes for two nonexpansive mappings and a mapping which satisfies condition C. Next, we consider strong convergence theorem of an implicit-shrinking iterative process for two nonexpansive mappings and a relative nonexpansive mapping on Banach spaces. Note that the conditions of strong convergence theorem are different from the strong convergence theorems for the implicit iterative processes in the literatures. Finally, we discuss a strong convergence theorem concerning two nonexpansive mappings and the resolvent of a maximal monotone operator in a Banach space.

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Author: Lai-Jiu Lin - Chih-Sheng Chuang - Zenn-Tsun Yu

Source: https://link.springer.com/







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