Abstract. We study weak convergence of implicit iterations for a countable family of continuous pseudocontractive mappings and a nonexpansive mapping in Banach spaces. Moreover, necessary and sufficient conditions for strong convergence to a common fixed point of continuous hemicontractive mappings and a continuous quasi-nonexpansive mapping are given in real Banach spaces. The obtained results extend those announced by many authors.

Received: February 5, 2013

AMS Subject Classification: 47H09, 47H10

Key Words and Phrases: implicit iteration, pseudocontractive mappings, hemicontractive mappings, common fixed points, weak and strong convergence theorems

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DOI: 10.12732/ijpam.v85i3.9 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 85
Issue: 3

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