The method of cyclic resolvents for quasi-convex functions and quasi-nonexpansive mappings

Abstract

The method of cyclic resolvents has been extended for a finite family of quasi-convex functions and quasi-nonexpansive mappings in Hadamard spaces. The essential tool for proving the main results is the use of the recent article by the first author and Mohebbi on the behavior of an iteration of a strongly quasi-nonexpansive sequence. The results are new even in Hilbert spaces.