Open Access

Erratum to: Common Fixed Point Theorems for Hybrid Pairs of Occasionally Weakly Compatible Mappings Satisfying Generalized Contractive Condition of Integral Type Revisited

Fixed Point Theory and Applications20082008:274793

https://doi.org/10.1155/2008/274793

Received: 3 September 2008

Accepted: 30 September 2008

Published: 11 November 2008

The original article was published in Fixed Point Theory and Applications 2007 2007:054101

We are indebted to Valeriu Popa for pointing out our error in [1]. In looking again at the paper, we came up with the following example.

Let with the usual metric, and define by . Since , every point is a coincidence point, and . Also, for all and , and for , so and satisfy the hypotheses of all theorems and corollaries in [1], but and have no common fixed point.

Thus, it is not surprising that there are a number of papers involving hybrid pairs in which the conclusion of the theorems is not a common fixed point, but a common coincidence point (see, e.g., [210]). To obtain a common fixed point, a number of theorems assume the strong condition that the common coincidence point is also a fixed point of one of the maps.

Notes

Authors’ Affiliations

(1)
Centre for Advanced Studies in Mathematics and Department of Mathematics, Lahore University of Management Sciences
(2)
Department of Mathematics, Indiana University

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Copyright

© M. Abbas and B. E. Rhoades. 2008

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.