A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces
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...
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| Format: | Article |
| Language: | English |
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Naim Çağman
2023-06-01
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| Series: | Journal of New Theory |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/3059372 |
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| _version_ | 1849723677943267328 |
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| author | Tarapada Bag Abhishikta Das |
| author_facet | Tarapada Bag Abhishikta Das |
| author_sort | Tarapada Bag |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e4a21f92c7e54994bd2d14ee91aeef2b |
| institution | DOAJ |
| issn | 2149-1402 |
| language | English |
| publishDate | 2023-06-01 |
| publisher | Naim Çağman |
| record_format | Article |
| series | Journal of New Theory |
| spelling | doaj-art-e4a21f92c7e54994bd2d14ee91aeef2b2025-08-20T03:10:57ZengNaim ÇağmanJournal of New Theory2149-14022023-06-0143738210.53570/jnt.12770262425A Note on Equivalence of G-Cone Metric Spaces and G-Metric SpacesTarapada Bag0https://orcid.org/0000-0002-8834-7097Abhishikta Das1https://orcid.org/0000-0002-2860-424XSiksha-Bhavana, Visva-BharatiDepartment of Mathematics, Siksha-Bhavana, Visva-BharatiThis 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.https://dergipark.org.tr/en/download/article-file/3059372g-metric spaceg-cone metric spacetvs-g cone metric space |
| spellingShingle | Tarapada Bag Abhishikta Das A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces Journal of New Theory g-metric space g-cone metric space tvs-g cone metric space |
| title | A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces |
| title_full | A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces |
| title_fullStr | A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces |
| title_full_unstemmed | A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces |
| title_short | A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces |
| title_sort | note on equivalence of g cone metric spaces and g metric spaces |
| topic | g-metric space g-cone metric space tvs-g cone metric space |
| url | https://dergipark.org.tr/en/download/article-file/3059372 |
| work_keys_str_mv | AT tarapadabag anoteonequivalenceofgconemetricspacesandgmetricspaces AT abhishiktadas anoteonequivalenceofgconemetricspacesandgmetricspaces AT tarapadabag noteonequivalenceofgconemetricspacesandgmetricspaces AT abhishiktadas noteonequivalenceofgconemetricspacesandgmetricspaces |