A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces
Authors : Abhishikta Das, Tarapada Bag
Pages : 73-82
Doi:10.53570/jnt.1277026
View : 30 | Download : 34
Publication Date : 2023-06-30
Article Type : Research Article
Abstract :This paper contains the equivalence between tvs-G cone metric and G-metric using a scalarization function $\\zeta_p$, defined over a locally convex Hausdorff topological vector space. This function ensures that most studies on the existence and uniqueness of fixed-point theorems on G-metric space and tvs-G cone metric spaces are equivalent. We prove the equivalence between the vector-valued version and scalar-valued version of the fixed-point theorems of those spaces. Moreover, we present that if a real Banach space is considered instead of a locally convex Hausdorff space, then the theorems of this article extend some results of G-cone metric spaces and ensure the correspondence between any G-cone metric space and the G-metric space.Keywords : G-metric space, G-cone metric space, tvs-G cone metric space