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

Abhishikta Das; Tarapada Bag

doi:10.53570/jnt.1277026

EN

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

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

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Abhishikta Das ^*
0000-0002-2860-424X
India

Tarapada Bag
0000-0002-8834-7097
India

Publication Date

June 30, 2023

Submission Date

April 4, 2023

Acceptance Date

June 21, 2023

Published in Issue

Year 2023 Number: 43

DOI

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

IZ

https://izlik.org/JA59BF93ZB

APA

Das, A., & Bag, T. (2023). A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces. Journal of New Theory, 43, 73-82. https://doi.org/10.53570/jnt.1277026

AMA

1.Das A, Bag T. A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces. JNT. 2023;(43):73-82. doi:10.53570/jnt.1277026

Chicago

Das, Abhishikta, and Tarapada Bag. 2023. “A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces”. Journal of New Theory, nos. 43: 73-82. https://doi.org/10.53570/jnt.1277026.

EndNote

Das A, Bag T (June 1, 2023) A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces. Journal of New Theory 43 73–82.

IEEE

[1]A. Das and T. Bag, “A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces”, JNT, no. 43, pp. 73–82, June 2023, doi: 10.53570/jnt.1277026.

ISNAD

Das, Abhishikta - Bag, Tarapada. “A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces”. Journal of New Theory. 43 (June 1, 2023): 73-82. https://doi.org/10.53570/jnt.1277026.

JAMA

1.Das A, Bag T. A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces. JNT. 2023;:73–82.

MLA

Das, Abhishikta, and Tarapada Bag. “A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces”. Journal of New Theory, no. 43, June 2023, pp. 73-82, doi:10.53570/jnt.1277026.

Vancouver

1.Abhishikta Das, Tarapada Bag. A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces. JNT. 2023 Jun. 1;(43):73-82. doi:10.53570/jnt.1277026