An iterative method for variational inequality problems and fixed point problems in Hilbert spaces

Xiaolong Qin, Meijuan Shang, Yongfu Su

In this paper, we introduce a new iterative scheme to investigate the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a relaxed $(\gamma,r)$-cocoercive, Lipschitz continuous mapping. Our results improve and extend the corresponding results of many others.