Research Article Strong and Δ-Convergence Theorems for Common Fixed Points of a Finite Family of Multivalued Demicontractive Mappings in CAT(0) Spaces C. E. Chidume, A. U. Bello, and P. Ndambomve African University of Science and Technology, Abuja, Nigeria Correspondence should be addressed to C. E. Chidume; cchidume@aust.edu.ng Received 1 June 2014; Revised 16 July 2014; Accepted 18 July 2014; Published 16 October 2014 Academic Editor: Simeon Reich Copyright © 2014 C. E. Chidume et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Let K be a nonempty closed and convex subset of a complete CAT(0) space. Let   :→ CB (),=1,2,...,, be a family of multivalued demicontractive mappings such that  := ⋂  =1 (  )̸ =0. A Krasnoselskii-type iterative sequence is shown to Δ- converge to a common fxed point of the family {  ,=1,2,...,}. Strong convergence theorems are also proved under some additional conditions. Our theorems complement and extend several recent important results on approximation of fxed points of certain nonlinear mappings in CAT(0) spaces. Furthermore, our method of the proof is of special interest. 1. Introduction A metric space (,) is said to be a CAT(0) space if it is geodesically connected and if every geodesic triangle in  is at least as “thin” as its comparison triangle in the Euclidean space. It is well known that pre-Hilbert spaces, R-trees (see [1]), and Euclidean buildings (see, e.g., [2]) are among examples of CAT(0) spaces. For a thorough discussion of these spaces and the fundamental role they play in various branches of mathematics see Bridson and Haefiger [1] or Burago et al. [3]. Fixed point theory in CAT(0) spaces was frst studied by Kirk (see [4, 5]). He showed that every nonexpansive mapping defned on a nonempty closed convex and bounded subset of a CAT(0) space always has a fxed point. Since then, the fxed point theory for single-valued and multivalued mappings has received much attention (see, e.g., [6–13]). In 1976, Lim [14] introduced a notion of convergence in a general metric space which he called Δ-convergence (see Defnition 8). In 2008, Kirk and Panyanak [15] specialized Lim’s concept to CAT(0) spaces and showed that many results which involve weak convergence (e.g., Opial property and Kadec-Klee property) have precise analogs in this setting. Later on, Dhompongsa and Panyanak [16] obtained Δ-convergence theorems for the Picard, Mann, and Ishikawa iterations involving one mapping in the CAT(0) space setting. In [17], Chidume et al. introduced the class of multivalued -strictly pseudocontractive mappings which is a general- ization of the class of multivalued nonexpansive mappings in Hilbert spaces. Tey constructed a Krasnoselskii-type algorithm sequence and showed that it is an approximate fxed point sequence of the map. In particular, they proved the following theorem. Teorem 1 (Teorem 3.1 of [17]). Let  be a nonempty, closed, and convex subset of a real Hilbert space . Suppose that  :  → () is a multivalued -strictly pseudocontractive mapping such that () ̸ =0. Assume that () = {} for all  ∈ (). Let {  } be a sequence defned by  0 ∈  +1 =(1−)  +   , (1) where   ∈   and ∈(0,1). Ten, lim →∞ (  ,  )=0. Very recently, Chidume and Ezeora extended the result of Chidume et al. [17] to a fnite family of multivalued - strictly pseudocontractive mappings in real Hilbert spaces. Te following theorem is their main result. Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2014, Article ID 805168, 6 pages http://dx.doi.org/10.1155/2014/805168