A Modified Proximal Point Algorithm for Finite Families of Minimization Problems and Fixed Point Problems of Asymptotically Quasi-nonexpansive Multivalued Mappings

Abstract

ln this paper, a new iterative algorithm for finding common elements of the set of fixed points for a finite family of asymptotically quasinonexpansive multivalued mappings and the set of minimizers for a finite family of minimization problem is constructed. Under mild conditions on the control sequences, strong convergence of our algorithm was achieved without necessarily imposing any compactness condition on the space or the operator by using an independent approach. Our results improve, extend and generalize many important results recently announced in current literature.