Common fixed point of mappings satisfying rational inequality in complex valued metric space (Q2893007)

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scientific article; zbMATH DE number 6049630
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Common fixed point of mappings satisfying rational inequality in complex valued metric space
scientific article; zbMATH DE number 6049630

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    25 June 2012
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    common fixed point
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    complex valued metric space
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    Common fixed point of mappings satisfying rational inequality in complex valued metric space (English)
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    Let \((X,d)\) be a complete complex metric space in the sense of \textit{A. Azam, B. Fisher} and \textit{M. Khan} [Numer.\ Funct.\ Anal.\ Optim.\ 32, No.\ 3, 243--253 (2011; Zbl 1245.54036)]. The authors claim that they have proved the following theorem. If the mappings \(S,T:X\to X\) satisfy the condition \(d(Sx,Ty)\leq\{a[d(x,Sx)d(x,Ty)+d(y,Ty)d(y,Sx)]\}/\{d(x,Ty)+d(y,Sx)\}\) for some \(0\leq a<1\) and all \(x,y\in X\), then \(S\) and \(T\) have a unique common fixed point. The ``proof'' is incorrect in several places. No examples are given.
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