Some results on non-expansive mappings and relaxed cocoercive mappings in Hilbert spaces
Xiaolong Qin, Yeol Je Cho, Shin Min Kang · Applicable Analysis · 2009
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.