Document Zbl 1541.54032

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Funct. Spaces</a> <a href="/?q=in%3A458824" title="Articles in this Issue">2021, Article ID 5525472, 11 p. (2021)</a>. </div> <div class="abstract">Summary: We introduce the notions of a generalized $\Theta$-contraction, a generalized $\Theta_{\mathcal{E}}$-weak contraction, a $\Psi_{\mathcal{E}}$-weak JS-contraction, an integral-type $\Theta_{\mathcal{E}}$-weak contraction, and an integral-type $\Psi_{\mathcal{E}}$-weak JS-contraction to establish the fixed point, fixed ellipse, and fixed elliptic disc theorems. Further, we verify these by illustrative examples with geometric interpretations to demonstrate the authenticity of the postulates. The motivation of this work is the fact that the set of nonunique fixed points may include a geometric figure like a circle, an ellipse, a disc, or an elliptic disc. Towards the end, we provide an application of $\Theta$-contraction to chemical sciences.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7355388">Cited in <strong>8</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A54H25" title="MSC2020">54H25</a> </td> <td class="space"> Fixed-point and coincidence theorems (topological aspects) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A54E40" title="MSC2020">54E40</a> </td> <td class="space"> Special maps on metric spaces </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A92E99" title="MSC2020">92E99</a> </td> <td class="space"> Chemistry </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ageneralised+%5C%28%5CTheta%5C%29-contraction">generalised $\Theta$-contraction</a>; <a href="/?q=ut%3Ageneralised+%5C%28%5CTheta_%7B%5Cmathcal%7BE%7D%7D%5C%29-weak+contraction">generalised $\Theta_{\mathcal{E}}$-weak contraction</a>; <a href="/?q=ut%3A%5C%28%5CPsi_%7B%5Cmathcal%7BE%7D%7D%5C%29-weak+JS-contraction">$\Psi_{\mathcal{E}}$-weak JS-contraction</a>; <a href="/?q=ut%3Aintegral-type+%5C%28%5CTheta_%7B%5Cmathcal%7BE%7D%7D%5C%29-weak+contraction">integral-type $\Theta_{\mathcal{E}}$-weak contraction</a>; <a href="/?q=ut%3Aintegral-type+%5C%28%5CPsi_%7B%5Cmathcal%7BE%7D%7D%5C%29-weak+JS-contraction">integral-type $\Psi_{\mathcal{E}}$-weak JS-contraction</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 1541.54032" data-ciurl="/ci/07355388" data-biburl="/bibtex/07355388.bib" data-amsurl="/amsrefs/07355388.bib" data-xmlurl="/xml/07355388.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07355388.pdf" title="Zbl 1541.54032 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/10.1155/2021/5525472" aria-label="DOI for “On unique and nonunique fixed points in metric spaces and application to chemical sciences”" title="10.1155/2021/5525472">DOI</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Aydi, H.; Tas, N.; Özgür, N. Y.; Mlaiki, N., Fixed-discs in rectangular metric spaces, Symmetry, 11, 2, 294 (2019) · <a href="/1416.54020" class="nowrap">Zbl 1416.54020</a> · <a href="https://doi.org/10.3390/sym11020294" class="nowrap">doi:10.3390/sym11020294</a></td> </tr><tr> <td>[2]</td> <td class="space">Bisht, R.; Özgür, N. Y., Geometric properties of discontinuous fixed point set of (ε-δ) contractions and applications to neural networks, Aequationes Math., 94, 5, 847-863 (2019) · <a href="/1502.54023" class="nowrap">Zbl 1502.54023</a></td> </tr><tr> <td>[3]</td> <td class="space">Joshi, M.; Tomar, A.; Padaliya, S. K., Fixed point to fixed disc and application in partial metric spaces, Chapter in a book “Fixed Point Theory and Its Applications to Real World Problem” (2021), New York, USA: Nova Science Publishers, New York, USA, ISBN: 978-1-53619-336-7 · <a href="/1499.54002" class="nowrap">Zbl 1499.54002</a></td> </tr><tr> <td>[4]</td> <td class="space">Joshi, M.; Tomar, A.; Padaliya, S. K., On geometric properties of non-unique fixed points in b-metric spaces, Chapter in a book “Fixed Point Theory and Its Applications to Real World Problem” (2021), New York, USA: Nova Science Publishers, New York, USA, ISBN: 978-1-53619-336-7 · <a href="/1499.54002" class="nowrap">Zbl 1499.54002</a></td> </tr><tr> <td>[5]</td> <td class="space">Joshi, M.; Tomar, A.; Padaliya, S. K., Fixed point to fixed ellipse in metric spaces and discontinuous activation function, Applied Mathematics. E-Notes, 1, 15 (2020)</td> </tr><tr> <td>[6]</td> <td class="space">Mlaiki, N.; Tas, N.; Özgür, N. Y., On the fixed-circle problem and Khan type contractions, Axioms, 7, 4, 80 (2018) · <a href="/1432.54069" class="nowrap">Zbl 1432.54069</a> · <a href="https://doi.org/10.3390/axioms7040080" class="nowrap">doi:10.3390/axioms7040080</a></td> </tr><tr> <td>[7]</td> <td class="space">Mlaiki, N.; Çelik, U.; Tas, N.; Özgür, N. Y.; Mukheimer, A., Wardowski type contractions and the fixed-circle problem on S-metric spaces, Journal of Mathematics, 2018 (2018) · <a href="/1487.54067" class="nowrap">Zbl 1487.54067</a></td> </tr><tr> <td>[8]</td> <td class="space">Mlaiki, N.; Tas, N.; Özgür, N. Y., New fixed-point theorems on an S-metric space via simulation functions, Mathematics, 7, 7, 583 (2019)</td> </tr><tr> <td>[9]</td> <td class="space">Mlaiki, N.; Özgür, N. Y.; Tas, N., New fixed-circle results related to Fc-contractive and Fc-expanding mappings on metric spaces (2021), https://arxiv.org/abs/2101.10770</td> </tr><tr> <td>[10]</td> <td class="space">Ochkov, V.; Nori, M.; Borovinskaya, E.; Reschetilowski, W., A new ellipse or math porcelain service, Symmetry, 11, 2, 184 (2019)</td> </tr><tr> <td>[11]</td> <td class="space">Özgür, N. Y.; Tas, N.; Çelik, U., Some fixed-circle results on S-metric spaces, Bulletin of Mathematical Analysis and Applications, 9, 2, 10-23 (2017) · <a href="/07041498" class="nowrap">Zbl 07041498</a></td> </tr><tr> <td>[12]</td> <td class="space">Özgür, N. Y.; Tas, N., Some fixed-circle theorems on metric spaces, Bulletin of the Malaysian Mathematical Sciences Society, 42, 4, 1433-1449 (2017) · <a href="/07093438" class="nowrap">Zbl 07093438</a></td> </tr><tr> <td>[13]</td> <td class="space">Özgür, N. Y.; Tas, N., Some fixed-circle theorems and discontinuity at fixed circle, AIP Conference Proceedings, 1926, article 020048, 1 (2018), AIP Publishing LLC · <a href="/1469.54168" class="nowrap">Zbl 1469.54168</a></td> </tr><tr> <td>[14]</td> <td class="space">Özgür, N. Y., Fixed-disc results via simulation functions, Turkish Journal of Mathematics, 43, 6, 2794-2805 (2019) · <a href="/1434.54017" class="nowrap">Zbl 1434.54017</a></td> </tr><tr> <td>[15]</td> <td class="space">Özgür, N. 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Y.; Mlaiki, N., New types of Fc-contractions and the fixed-circle problem, Mathematics, 6, 10, 188 (2018) · <a href="/1515.54034" class="nowrap">Zbl 1515.54034</a></td> </tr><tr> <td>[18]</td> <td class="space">Tas, N., Bilateral-type solutions to the fixed-circle problem with rectified linear units application, Turkish Journal of Mathematics, 44, 4, 1330-1344 (2020) · <a href="/1444.54039" class="nowrap">Zbl 1444.54039</a></td> </tr><tr> <td>[19]</td> <td class="space">Tomar, A.; Joshi, M., Near fixed point, near fixed interval circle and near fixed interval disc in metric interval space, Chapter in a book “Fixed Point Theory and Its Applications to Real World Problem” (2021), New York, USA: Nova Science Publishers, New York, USA, ISBN: 978-1-53619-336-7</td> </tr><tr> <td>[20]</td> <td class="space">Tomar, A.; Joshi, M.; Padaliya, S. K., Fixed point to fixed circle and activation function in partial metric space, Journal of Applied Analysis, 1 (2020)</td> </tr><tr> <td>[21]</td> <td class="space">Hussain, A.; Al-Sulami, H.; Hussain, N.; Farooq, H., Newly fixed disc results using advanced contractions on F-metric space, Journal of Applied Analysis & Computation, 10, 6, 2313-2322 (2020) · <a href="/1473.54054" class="nowrap">Zbl 1473.54054</a> · <a href="https://doi.org/10.11948/20190197" class="nowrap">doi:10.11948/20190197</a></td> </tr><tr> <td>[22]</td> <td class="space">Joshi, M.; Tomar, A.; Nabwey, H. A.; George, R., On unique and nonunique fixed points and fixed circles in $\mathcal{M}_v^b$-metric space and application to cantilever beam problem, Journal of Function Spaces, 2021 (2021) · <a href="/1498.54072" class="nowrap">Zbl 1498.54072</a> · <a href="https://doi.org/10.1155/2021/6681044" class="nowrap">doi:10.1155/2021/6681044</a></td> </tr><tr> <td>[23]</td> <td class="space">Saleh, H. N.; Sessa, S.; Alfaqih, W. M.; Imdad, M.; Mlaiki, N., Fixed circle and fixed disc results for new types of Θc-contractive mappings in metric spaces, Symmetry, 12, 11, 1825 (2020) · <a href="https://doi.org/10.3390/sym12111825" class="nowrap">doi:10.3390/sym12111825</a></td> </tr><tr> <td>[24]</td> <td class="space">Fréchet, M., Sur quelques points du calcul fonctionnel, palemo (30 via Ruggiero) (1906)</td> </tr><tr> <td>[25]</td> <td class="space">Jleli, M.; Samet, B., A new generalization of the Banach contraction principle, Journal of inequalities and applications, 2014 (2014) · <a href="/1322.47052" class="nowrap">Zbl 1322.47052</a></td> </tr><tr> <td>[26]</td> <td class="space">Ćirić, L. B., Generalised contractions and fixed-point theorems, Publications de l’Institut Mathématique, 12, 26, 9-26 (1971) · <a href="/0234.54029" class="nowrap">Zbl 0234.54029</a></td> </tr><tr> <td>[27]</td> <td class="space">Banach, S., Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae, 3, 133-181 (1922) · <a href="/48.0201.01" class="nowrap">JFM 48.0201.01</a> · <a href="https://doi.org/10.4064/fm-3-1-133-181" class="nowrap">doi:10.4064/fm-3-1-133-181</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"> © 2025 <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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