Abstract and Applied Analysis
Volume 2013 (2013), Article ID 629468, 10 pages
http://dx.doi.org/10.1155/2013/629468
Research Article

Convergence Theorems for Fixed Points of Multivalued Strictly Pseudocontractive Mappings in Hilbert Spaces

C. E. Chidume,1 C. O. Chidume,2 N. Djitté,3 and M. S. Minjibir1,4

1Mathematics Institute, African University of Science and Technology, PMB 681, Garki, Abuja, Nigeria
2Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, USA
3Université Gaston Berger, 234 Saint Louis, Senegal
4Department of Mathematical Sciences, Bayero University, PMB 3011, Kano, Nigeria

Received 10 September 2012; Accepted 15 April 2013

Academic Editor: Josef Diblík

Copyright © 2013 C. E. Chidume et al. This 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.

Abstract

Let be a nonempty, closed, and convex subset of a real Hilbert space . Suppose that is a multivalued strictly pseudocontractive mapping such that . A Krasnoselskii-type iteration sequence is constructed and shown to be an approximate fixed point sequence of ; that is, holds. Convergence theorems are also proved under appropriate additional conditions.