Proximal point algorithms for finding common fixed points of a finite family of quasi-nonexpansive multi-valued mappings in real Hilbert spaces

Abstract

In this paper, we propose a modified proximal point algorithm for finding a common element of the set of common fixed points of a finite family of quasi-nonexpansive multi-valued mappings and the set of minimizers of convex and lower semi-continuous functions. We obtain weak and strong convergence of the proposed algorithm to a common element of the two sets in real Hilbert spaces. A numerical example to support our main results is also given.