Common fixed points for some generalized multivalued nonexpansive mappings in uniformly convex metric spaces

Abkar and Eslamian (Nonlinear Anal. TMA, 74, 1835-1840, 2011) prove that if K is a nonempty bounded closed convex subset of a complete CAT(0) space X, t : K → K is a single-valued quasi-nonexpansive mapping and T : K → KC(K) is a multivalued mapping satisfying conditions (E) and (Cλ) for some λ ∈ (0, 1) such that t and T commute weakly, then there exists a point z ∈ K such that z = t(z) ∈ T(z). In this paper, we extend this result to the general setting of uniformly convex metric spaces. Nevertheless, condition (E) of T can be weakened to the strongly demiclosedness of I - T.