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Erschienen in:
2015 | OriginalPaper | Buchkapitel
8. New Approaches to Fixed Point Results on G-Metric Spaces
verfasst von : Ravi P. Agarwal, Erdal Karapınar, Donal O’Regan, Antonio Francisco Roldán-López-de-Hierro
Erschienen in: Fixed Point Theory in Metric Type Spaces
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Abstract
Recently, Samet et al. [184], and Jleli and Samet [97], observed that some fixed point theorems in the context of G-metric space in the literature can be concluded from existence results in the setting of quasi-metric spaces. In fact, if the contractivity condition of the fixed point theorem on a G-metric space can be reduced to two variables instead of there variables, then one can construct an equivalent fixed point theorem in the setup of usual metric spaces. More precisely, in [97, 184], the authors noticed that q(x, y) = G(x, y, y) forms a quasi-metric.