New Approaches to Fixed Point Results on G-Metric Spaces

Ravi P. Agarwal, Erdal Karapınar, Donal O’Regan and Antonio Francisco Roldán-López- de-Hierro
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Ravi P. Agarwal: Texas A&M University-Kingsville, Department of Mathematics
Erdal Karapınar: Atilim University, Department of Mathematics
Donal O’Regan: National University of Ireland
Antonio Francisco Roldán-López- de-Hierro: University of Granada, Department of Quantitative Methods for Economics and Business

Chapter Chapter 8 in Fixed Point Theory in Metric Type Spaces, 2015, pp 199-217 from Springer

Abstract: 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.

Keywords: Fixed Point Results; Quasi-metric Space; Contractivity Condition; Recall Definition; Admissible Functions (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-24082-4_8

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