Invariant approximations for commuting mappings in CAT(0) and hyperconvex spaces

In this paper, for a commuting pair consisting of a point-valued nonexpansive self-mapping t and a set-valued nonexpansive selfmapping T of a hyperconvex metric space (or a CAT(0) space) X, we look for a solution to the problem of existence of z ∈ E ⊂ X such that d(z,y) = d(y,E) and z = t (z) ∈ T (z). © 2007 Elsevier Inc. All rights reserved