SELECTIVE INERTIAL BLOCK-ITERATIVE SCHEMES FOR A CLASS OF VARIATIONAL INEQUALITIES AND APPLICATIONS

Abstract

Our purpose in this paper is to present inertial block-iterative schemes with selective technique for finding a solution of a variational inequality problem over the set of common fixed points of a finite family of demiclosed quasinonexpansive mappings in Hilbert spaces. First, we introduce a basic scheme and show that any sequence, generated by this scheme, converges weakly to a point in the common fixed point set. Then, based on a specific combination of the scheme with the steepest-descent method, we propose new schemes, strong convergence of which is proved without the approximately shrinking and boundedly regular assumptions on the mappings and their fixed point sets, respectively, that are usually required recently in literature. An application to study a networked system and computational experiments are given for illustration and comparison