Document Zbl 07892716

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Math. Res. Appl.</a> <a href="/?q=in%3A515666" title="Articles in this Issue">44, No. 3, 397-407 (2024)</a>. </div> <div class="abstract">Summary: In this paper, we mainly study fuzzy (quasi-)pseudo-$b$-metrics on algebraic structures. We mainly establish the following results: (1) If a group $G$ with a topology $\tau$, which is induced by a left invariant fuzzy quasi-pseudo-$b$-metric (resp., pseudo-$b$-metric) on the $G$, is a right topological group, then $G$ with the topology $\tau$ is a paratopological group (resp., a topological group) and (2) If a semigroup $S$ with a topology $\tau$ is induced by an invariant fuzzy quasi-pseudo-$b$-metric, then $S$ with the topology $\tau$ is a topological semigroup.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A54E99" title="MSC2020">54E99</a> </td> <td class="space"> Topological spaces with richer structures </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A54H11" title="MSC2020">54H11</a> </td> <td class="space"> Topological groups (topological aspects) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A54H15" title="MSC2020">54H15</a> </td> <td class="space"> Transformation groups and semigroups (topological aspects) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A54A40" title="MSC2020">54A40</a> </td> <td class="space"> Fuzzy topology </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aleft+topological+group">left topological group</a>; <a href="/?q=ut%3Aright+topological+group">right topological group</a>; <a href="/?q=ut%3Asemitopological+group">semitopological group</a>; <a href="/?q=ut%3Apara-topological+group">para-topological group</a>; <a href="/?q=ut%3Atopological+group">topological group</a>; <a href="/?q=ut%3Atopological+semigroup">topological semigroup</a>; <a href="/?q=ut%3Afuzzy+quasi-pseudo-%5C%28b%5C%29-metric">fuzzy quasi-pseudo-$b$-metric</a>; <a href="/?q=ut%3Ainvariant+fuzzy+%28quasi-%29pseudo-%5C%28b%5C%29-metric">invariant fuzzy (quasi-)pseudo-$b$-metric</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 07892716" data-ciurl="/ci/07892716" data-biburl="/bibtex/07892716.bib" data-amsurl="/amsrefs/07892716.bib" data-xmlurl="/xml/07892716.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07892716.pdf" title="Zbl 07892716 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.3770/j.issn:2095-2651.2024.03.010" aria-label="DOI for “Fuzzy quasi-pseudo-$b$-metrics on algebraic structures”" title="10.3770/j.issn:2095-2651.2024.03.010">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">M. M. FR ÉCHET. Sur quelques points du calcul fonctionnel. Rend. Circ. Mat. Palerm., 1906, 22(1): 1-72. · <a href="/37.0348.02" class="nowrap">JFM 37.0348.02</a></td> </tr><tr> <td>[2]</td> <td class="space">S. CZERWIK. Contraction mappings in b-metric spaces. Acta Math. Inform. Univ. Ostra., 1993, 1: 5-11. · <a href="/0849.54036" class="nowrap">Zbl 0849.54036</a></td> </tr><tr> <td>[3]</td> <td class="space">M. BORICEANU, A. PETRUSEL, I. A. RUS. Fixed point theorems for some multivalued generalized con-tractions in b metric spaces. Int. J. Math. Stat., 2010, 6: 65-76.</td> </tr><tr> <td>[4]</td> <td class="space">M. BORICEANU, M. BOTA, A. PETRUSEL. Multivalued fractals in b-metric spaces. Cent. Eur. J. Math., 2010, 8(2): 367-377. · <a href="/1235.54011" class="nowrap">Zbl 1235.54011</a></td> </tr><tr> <td>[5]</td> <td class="space">M. BORICEANU. Strict fixed point theorems for multivalued operators in b-metric spaces. Int. J. Mod. Math., 2009, 4: 285-301. · <a href="/1221.54051" class="nowrap">Zbl 1221.54051</a></td> </tr><tr> <td>[6]</td> <td class="space">S. L. SINGH, B. PRASAD. Some coincidence theorems and stability of iterative procedures. Comput. Math. Appl.,2008, 55: 2512-2520. · <a href="/1142.65360" class="nowrap">Zbl 1142.65360</a></td> </tr><tr> <td>[7]</td> <td class="space">L. A. ZADEH. Fuzzy Sets. Inf. Contr., 1965, 8: 338-353. · <a href="/0139.24606" class="nowrap">Zbl 0139.24606</a></td> </tr><tr> <td>[8]</td> <td class="space">I. KRAMOSIL, J. MICH ÁLEK. Fuzzy metrics and statistical metric spaces. Kybernetika, 1975, 11: 336-344. · <a href="/0319.54002" class="nowrap">Zbl 0319.54002</a></td> </tr><tr> <td>[9]</td> <td class="space">B. SCHWEIZER, A. SKLAR. Statistical metric spaces. Pacific J. Math., 1960, 10: 313-334. · <a href="/0091.29801" class="nowrap">Zbl 0091.29801</a></td> </tr><tr> <td>[10]</td> <td class="space">A. GEORGE, P. VEERAMANI. On some results of analysis for fuzzy metric spaces. Fuzzy Sets Syst., 1997, 90(3): 365-368. · <a href="/0917.54010" class="nowrap">Zbl 0917.54010</a></td> </tr><tr> <td>[11]</td> <td class="space">V. GREGORI, S. ROMAGUERA. Fuzzy quasi-metric spaces. Appl. Gen. Topol., 2004, 5(1): 129-136. · <a href="/1076.54005" class="nowrap">Zbl 1076.54005</a></td> </tr><tr> <td>[12]</td> <td class="space">S. N Ǎd ǍBAN. Fuzzy b-metric spaces. Int. J. Comput. Commun., 2016, 11: 273-281.</td> </tr><tr> <td>[13]</td> <td class="space">I.</td> </tr><tr> <td>[14]</td> <td class="space">S ÁNCHEZ, M. SANCHIS. Fuzzy quasi-pseudometrics on algebraic structures. Fuzzy Sets Syst., 2018, 330: 79-86. · <a href="/1380.54012" class="nowrap">Zbl 1380.54012</a></td> </tr><tr> <td>[15]</td> <td class="space">M. PALUSZY ŃSKI, K. STEMPAK. On quasi-metric and metric spaces. P. Am. Math. Soc., 2009, 137(12): 4307-4312. · <a href="/1191.54022" class="nowrap">Zbl 1191.54022</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2024 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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