Erratum to: Common Fixed Point Theorems for Hybrid Pairs of Occasionally Weakly Compatible Mappings Satisfying Generalized Contractive Condition of Integral Type Revisited
© M. Abbas and B. E. Rhoades. 2008
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 . 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 , 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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