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Applicable Analysis
An International Journal
Volume 88, 2009 - Issue 1
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Original Articles

Some results on non-expansive mappings and relaxed cocoercive mappings in Hilbert spaces

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Pages 1-13 | Received 08 Oct 2007, Accepted 19 Jun 2008, Published online: 21 May 2009
 

Abstract

In this article, we introduce a new iterative scheme to investigate the problem of finding a common element of the set of common fixed points of a finite family of non-expansive mappings and the set of solutions of a variational inequality problem for a relaxed cocoercive mapping by viscosity approximate methods. Our results improve and extend the recent ones announced by Iiduka and Tahakshi [H. Iiduka, W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. 61 (2005), pp. 341–350] and many others.

2000 Mathematics Subject Classifications::

Acknowledgements

The project was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2007-313-C00040).

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