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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 Applications volume 2008, Article number: 274793 (2008) Cite this article

The Original Article was published on 10 September 2007

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., [2–10]). 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.

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Authors and Affiliations

  1. Centre for Advanced Studies in Mathematics and Department of Mathematics, Lahore University of Management Sciences, Lahore, 54792, Pakistan

    M. Abbas

  2. Department of Mathematics, Indiana University, Bloomington, IN, 47405, USA

    B. E. Rhoades

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  1. M. Abbas
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  2. B. E. Rhoades
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Correspondence to B. E. Rhoades.

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The online version of the original article can be found at 10.1155/2007/54101

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Abbas, M., Rhoades, B.E. 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 Appl 2008, 274793 (2008). https://doi.org/10.1155/2008/274793

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