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International Journal of Analysis
Volume 2014, Article ID 269786, 7 pages
http://dx.doi.org/10.1155/2014/269786
Research Article

Convergence Theorems for Fixed Points of Multivalued Mappings in Hilbert Spaces

Section de Mathématiques Appliquées, Université Gaston Berger, BP 234 Saint Louis, Senegal

Received 29 April 2014; Accepted 25 August 2014; Published 24 September 2014

Academic Editor: Remi Léandre

Copyright © 2014 N. Djitte and M. Sene. 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 real Hilbert space and a nonempty closed convex subset of . Suppose is a multivalued Lipschitz pseudocontractive mapping such that . An Ishikawa-type iterative algorithm is constructed and it is shown that, for the corresponding sequence , under appropriate conditions on the iteration parameters, holds. Finally, convergence theorems are proved under approximate additional conditions. Our theorems are significant improvement on important recent results of Panyanak (2007) and Sastry and Babu (2005).