Abstract
Abstract Using a combination of techniques introduced by Jleli and Samet (Fixed Point Theory Appl. 2012:210, 2012) and Samet et al. (Int. J. Anal. 2013:917158, 2013) on the one hand, and by Kadelburg et al. (Bull. Math. Anal. Appl. 4:51-63, 2012) on the other hand, we show that several coupled fixed point results in (ordered) G-metric spaces obtained recently are simple consequences of the respective standard (ordered) metric results. The technique can be applied both in symmetric and asymmetric cases. Moreover, we show by an example that the results thus obtained are usually stronger than those presented in the literature. MSC:47H10, 54H25.
Highlights
As one of fruitful generalizations of metric spaces, G-metric spaces were introduced by Mustafa and Sims in [ ]
It should be noted that there exist two kinds of G-metric spaces, symmetric and asymmetric ones, and while it was immediately clear that in the symmetric case these results can be reduced to their metric counterparts, in the asymmetric case, new proofs usually had to be found
The notion of a coupled fixed point for mappings with two variables was introduced in the articles [ – ]
Summary
As one of fruitful generalizations of metric spaces, G-metric spaces were introduced by Mustafa and Sims in [ ]. In the papers [ – ], the authors presented another technique which reduces coupled fixed point results in metric and various abstract metric spaces to the results for mappings with one variable.
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