Strong convergence of a general iterative method for variational inequality problems and fixed point problems in Hilbert spaces

摘要: Abstract In this paper, we introduce a new iterative scheme to investigate the problem of finding common element set fixed points finite family nonexpansive mappings and solutions variational inequality for relaxed cocoercive mapping by viscosity approximate methods. Our results improve extend recent ones announced Chen et al. [J.M. Chen, L.J. Zhang, T.G. Fan, Viscosity approximation methods monotone mappings, doi:10.1016/j.jmaa.2006.12.088], Iiduka Tahakshi [H. Iiduka, W. Takahashi, Strong convergence theorems inverse-strongly Nonlinear Anal. 61 (2005) 341–350], Yao [Y.H. Yao, J.C. On modified method Appl. Math. Comput, doi:10.1016/j.amc.2006.08.062] Many others.