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

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.

Keywords:

• projection method
• relaxed cocoercive mapping
• non-expansive mapping
• fixed point
• variational inequality

2000 Mathematics Subject Classifications::

• 47H05
• 47H09
• 47J25

Acknowledgements

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