Reconstruction of G-Metrics: G ^∗-Metrics

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.