Iterative Approximation of Common Fixed Points for Edge-Preserving Quasi-Nonexpansive Mappings in Hilbert Spaces along with Directed Graph

We present iterative approximation results of an iterative scheme for finding common fixed points of edge-preserving quasi-nonexpansive self-maps in Hilbert spaces along with directed graph. We obtain weak as well as strong convergence of our scheme under various assumptions. That is, we impose several possible mild conditions on the domain, on the mapping, or on the parameters involved in our scheme to prove convergence results. We support numerically our main outcome by giving an example. Eventually, an application is provided for solving a variational inequality problem. Our result are new/generalized some recently announced results of the literature.