Open Access

An Extension of Gregus Fixed Point Theorem

Fixed Point Theory and Applications20072007:078628

DOI: 10.1155/2007/78628

Received: 2 October 2006

Accepted: 17 December 2006

Published: 7 March 2007


Let be a closed convex subset of a complete metrizable topological vector space and a mapping that satisfies for all , where , , , , , and . Then has a unique fixed point. The above theorem, which is a generalization and an extension of the results of several authors, is proved in this paper. In addition, we use the Mann iteration to approximate the fixed point of .


Authors’ Affiliations

Mathematics Department, University of Lagos


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© J. O. Olaleru and H. Akewe. 2007

This article is published under license to BioMed Central Ltd. 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.