Reconstruction of G-Metrics: G ∗-Metrics

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 10 in Fixed Point Theory in Metric Type Spaces, 2015, pp 229-248 from Springer

Abstract: Abstract The main aim of the present chapter is to prove new unidimensional and multidimensional fixed point results in the framework of G-metric spaces provided with a partial preorder (not necessarily a partial order). However, we need to overcome the well-known fact that the usual product of G-metrics is not necessarily a G-metric unless they come from classical metrics. Hence, we will omit one of the axioms that define a G-metric and we consider a new class of metrics, called G ∗ -metrics. Notice that our main results are valid in the context of G-metric spaces.

Keywords: Partial Preorder; Classical Metrics; Quasi-metric Space; Symmetric Symmetry; Obvious Geometric Interpretation (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-24082-4_10

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