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...
Gespeichert in:
Veröffentlicht in: | Journal of New Theory 2023-06 (43), p.73-82 |
---|---|
Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | 82 |
---|---|
container_issue | 43 |
container_start_page | 73 |
container_title | Journal of New Theory |
container_volume | |
creator | DAS, Abhishikta BAG, Tarapada |
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. |
doi_str_mv | 10.53570/jnt.1277026 |
format | Article |
fullrecord | <record><control><sourceid>crossref</sourceid><recordid>TN_cdi_crossref_primary_10_53570_jnt_1277026</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_53570_jnt_1277026</sourcerecordid><originalsourceid>FETCH-LOGICAL-c756-26cf3ec3c858bc7cf153e88fc8add00e53d73cfe3260d34a0927945feff0acf83</originalsourceid><addsrcrecordid>eNpVj81Kw0AUhWehYKnd-QDzAKbe-Z8sQ6hVqLqw-zC9uRciNamZKPj2Bu3G1eGcDw58QtwoWDvjAty99dNa6RBA-wux0MqWhbKgr8Qq5-4A1nsdvLcLUVXyeZhIDr3cfHx2X-lIPc6V5baoh57kE01jh_L1lJCyTH07g3_btbjkdMy0OudS7O83-_qh2L1sH-tqV2BwvtAe2RAajC4eMCArZyhGxpjaFoCcaYNBJqM9tMYmKHUorWNihoQczVLc_t3iOOQ8EjensXtP43ejoPmVbmbp5ixtfgD3Kktz</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces</title><source>EZB-FREE-00999 freely available EZB journals</source><creator>DAS, Abhishikta ; BAG, Tarapada</creator><creatorcontrib>DAS, Abhishikta ; BAG, Tarapada</creatorcontrib><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.</description><identifier>ISSN: 2149-1402</identifier><identifier>DOI: 10.53570/jnt.1277026</identifier><language>eng</language><ispartof>Journal of New Theory, 2023-06 (43), p.73-82</ispartof><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c756-26cf3ec3c858bc7cf153e88fc8add00e53d73cfe3260d34a0927945feff0acf83</cites><orcidid>0000-0002-2860-424X ; 0000-0002-8834-7097</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>315,781,785,27926,27927</link.rule.ids></links><search><creatorcontrib>DAS, Abhishikta</creatorcontrib><creatorcontrib>BAG, Tarapada</creatorcontrib><title>A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces</title><title>Journal of New Theory</title><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.</description><issn>2149-1402</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNpVj81Kw0AUhWehYKnd-QDzAKbe-Z8sQ6hVqLqw-zC9uRciNamZKPj2Bu3G1eGcDw58QtwoWDvjAty99dNa6RBA-wux0MqWhbKgr8Qq5-4A1nsdvLcLUVXyeZhIDr3cfHx2X-lIPc6V5baoh57kE01jh_L1lJCyTH07g3_btbjkdMy0OudS7O83-_qh2L1sH-tqV2BwvtAe2RAajC4eMCArZyhGxpjaFoCcaYNBJqM9tMYmKHUorWNihoQczVLc_t3iOOQ8EjensXtP43ejoPmVbmbp5ixtfgD3Kktz</recordid><startdate>20230630</startdate><enddate>20230630</enddate><creator>DAS, Abhishikta</creator><creator>BAG, Tarapada</creator><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-2860-424X</orcidid><orcidid>https://orcid.org/0000-0002-8834-7097</orcidid></search><sort><creationdate>20230630</creationdate><title>A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces</title><author>DAS, Abhishikta ; BAG, Tarapada</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c756-26cf3ec3c858bc7cf153e88fc8add00e53d73cfe3260d34a0927945feff0acf83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><toplevel>online_resources</toplevel><creatorcontrib>DAS, Abhishikta</creatorcontrib><creatorcontrib>BAG, Tarapada</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of New Theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>DAS, Abhishikta</au><au>BAG, Tarapada</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces</atitle><jtitle>Journal of New Theory</jtitle><date>2023-06-30</date><risdate>2023</risdate><issue>43</issue><spage>73</spage><epage>82</epage><pages>73-82</pages><issn>2149-1402</issn><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.</abstract><doi>10.53570/jnt.1277026</doi><tpages>10</tpages><orcidid>https://orcid.org/0000-0002-2860-424X</orcidid><orcidid>https://orcid.org/0000-0002-8834-7097</orcidid><oa>free_for_read</oa></addata></record> |
fulltext | fulltext |
identifier | ISSN: 2149-1402 |
ispartof | Journal of New Theory, 2023-06 (43), p.73-82 |
issn | 2149-1402 |
language | eng |
recordid | cdi_crossref_primary_10_53570_jnt_1277026 |
source | EZB-FREE-00999 freely available EZB journals |
title | A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-18T09%3A55%3A53IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-crossref&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20Note%20on%20Equivalence%20of%20G-Cone%20Metric%20Spaces%20and%20G-Metric%20Spaces&rft.jtitle=Journal%20of%20New%20Theory&rft.au=DAS,%20Abhishikta&rft.date=2023-06-30&rft.issue=43&rft.spage=73&rft.epage=82&rft.pages=73-82&rft.issn=2149-1402&rft_id=info:doi/10.53570/jnt.1277026&rft_dat=%3Ccrossref%3E10_53570_jnt_1277026%3C/crossref%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |