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 : 35 | Download : 37

Publication Date : 2023-06-30

Article Type : Research Paper

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