Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 178421, 10 pages
doi:10.1155/2010/178421
Research Article

The Theory of Reich's Fixed Point Theorem for Multivalued Operators

Tania Lazăr,1 Ghiocel Moţ,2 Gabriela Petruşel,3 and Silviu Szentesi4

1Commercial Academy of Satu Mare, Mihai Eminescu Street No. 5, Satu Mare, Romania
2Aurel Vlaicu University of Arad, Elena Dragoi Street, No. 2, 310330 Arad, Romania
3Department of Business, Babeş-Bolyai University, Cluj-Napoca, Horea Street No. 7, 400174 Cluj-Napoca, Romania
4Aurel Vlaicu University of Arad, Revoulţiei Bd., No. 77, 310130 Arad, Romania

Received 12 April 2010; Revised 12 July 2010; Accepted 18 July 2010

Academic Editor: S. Reich

Copyright © 2010 Tania Lazăr 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

The purpose of this paper is to present a theory of Reich's fixed point theorem for multivalued operators in terms of fixed points, strict fixed points, multivalued weakly Picard operators, multivalued Picard operators, data dependence of the fixed point set, sequence of multivalued operators and fixed points, Ulam-Hyers stability of a multivalued fixed point equation, well-posedness of the fixed point problem, and the generated fractal operator.