HYBRID PROJECTION METHODS FOR THE GENERAL VARIATIONAL-LIKE INEQUALITY PROBLEMS

In this paper, we consider a general variational-like inequality problem. We use the generalized relaxed α-monotonicity defined by Preda et al., [15], and KKM technique to prove the existence of solutions of general variational-like inequalities in Banach spaces. Furthermore, we use a hybrid projection iteration scheme to find a common element of solutions of a general variational-like inequality problem for generalized relaxed α-monotone mappings and the set of fixed points of a finite family of quasi-∅- nonexpansive mappings in a uniformly smooth and uniformly convex Banach space.