Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 351531, 10 pages
Research Article

Existence and Approximation of Fixed Points for Set-Valued Mappings

Department of Mathematics, The Technion-Israel Institute of Technology, 32000 Haifa, Israel

Received 8 December 2009; Accepted 29 January 2010

Academic Editor: Tomonari Suzuki

Copyright © 2010 Simeon Reich and Alexander J. Zaslavski. 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.


Taking into account possibly inexact data, we study both existence and approximation of fixed points for certain set-valued mappings of contractive type. More precisely, we study the existence of convergent iterations in the presence of computational errors for two classes of set-valued mappings. The first class comprises certain mappings of contractive type, while the second one contains mappings satisfying a Caristi-type condition.