Inertial Iterative Process for Fixed Points of Certain Quasi-nonexpansive Mappings

This paper deals with a general formalism which consists in approximating a point in a nonempty set , in a real Hilbert space , by a sequence such that , where , are in and is a sequence included in a certain class of self-mappings on , such that every fixed point set of contains . This iteration method is inspired by an implicit discretization of the second order ‘heavy ball with friction’ dynamical system. Under suitable conditions on the parameters and the operators , we prove that this scheme generates a sequence which converges weakly to an element of . In particular, by appropriate choices of , this algorithm works for approximating common fixed points of infinite countable families of a wide class of operators which includes -averaged quasi-nonexpansive mappings for .