Steepest-descent block-iterative methods for a finite family of quasi-nonexpansive mappings

<p style='text-indent:20px;'>In this paper, for solving the variational inequality problem over set of common fixed points a finite family demiclosed quasi-nonexpansive mappings in Hilbert spaces, we propose two new strongly convergent methods, constructed by specific combinations between steepest-descent method and block-iterative ones. The strong convergence is proved without boundedly regular assumptions on point sets as well approximately shrinking property each mapping family, that are usually assumed recent literature similar problems. Applications to multiple-operator split (MOSCFPP) minimum lower semi-continuous convex functions with numerical experiments given.</p>