A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces

Year 2023, Issue: 43 , 73 - 82 , 30.06.2023

Abhishikta Das , Tarapada Bag

https://doi.org/10.53570/jnt.1277026

https://izlik.org/JA59BF93ZB

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

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