Document Zbl 1463.54109

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Math. Anal.</a> <a href="/?q=in%3A453326" title="Articles in this Issue">1, No. 2, 108-112 (2018)</a>. </div> <div class="abstract">Summary: In several recent papers, attempts have been made to apply Wardowski’s method of $F$-contractions in order to obtain fixed point results for single and multivalued mappings in $b$-metric spaces. In this article, it is shown that in most cases the conditions imposed on respective mappings are too strong and that the results can be obtained directly, i.e., without using most of the properties of auxiliary function $F$.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7251258">Cited in <strong>25</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></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3A%5C%28b%5C%29-metric+space">$b$-metric space</a>; <a href="/?q=ut%3A%5C%28F%5C%29-contraction">$F$-contraction</a>; <a href="/?q=ut%3A%5C%28%5Calpha%5C%29-admissible+mappings">$\alpha$-admissible mappings</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 1463.54109" data-ciurl="/ci/07251258" data-biburl="/bibtex/07251258.bib" data-amsurl="/amsrefs/07251258.bib" data-xmlurl="/xml/07251258.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07251258.pdf" title="Zbl 1463.54109 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/10.33205/cma.468813" aria-label="DOI for “Notes on some recent papers concerning $F$-contractions in $b$-metric spaces”" title="10.33205/cma.468813">DOI</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by-nc/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"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/nc.svg" alt="Creative Commons NC license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">H. Afshari, H. Aydi and E. Karapinar,On generalizedα-ψ-Geraghty contractions onb-metric spaces, Georgian Math. J., doi.org/10.1515/gmj-2017-0063. · <a href="/1437.54035" class="nowrap">Zbl 1437.54035</a></td> </tr><tr> <td>[2]</td> <td class="space">M. U. Ali, T. Kamran and M. Postolache,Solution of Volterra integral inclusion inb-metric spaces via new fixed point theorem, Nonlinear Anal. Model. Control,22(1) (2017), 17-30. · <a href="/1420.54062" class="nowrap">Zbl 1420.54062</a></td> </tr><tr> <td>[3]</td> <td class="space">I. A. Bakhtin,The contraction mapping principle in quasimetric spaces, Funct. Anal., Ulianowsk Gos. Ped. Inst.,30 (1989), 26-37. · <a href="/0748.47048" class="nowrap">Zbl 0748.47048</a></td> </tr><tr> <td>[4]</td> <td class="space">Lj. ´Ciri´c, V. Parvaneh and N. Hussain,Fixed point results for weaklyα-admissible pairs, Filomat,30(14) (2016), 3697- 3713. · <a href="/1461.54081" class="nowrap">Zbl 1461.54081</a></td> </tr><tr> <td>[5]</td> <td class="space">M. Cosentino, M. Jleli, B. Samet and C. Vetro,Solvability of integrodifferential problems via fixed point theory inb-metric spaces, Fixed Point Theory Appl.,70(2015), 1-15. · <a href="/1505.45010" class="nowrap">Zbl 1505.45010</a></td> </tr><tr> <td>[6]</td> <td class="space">S. Czerwik,Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav.,1(1993), 5-11. · <a href="/0849.54036" class="nowrap">Zbl 0849.54036</a></td> </tr><tr> <td>[7]</td> <td class="space">N. Hussain, M. A. Kutbi and P. Salimi,Fixed point theory inα-complete metric spaces with applications, Abstr. Appl. Anal., 2014, Article ID 280817, 1-11. · <a href="/1429.54051" class="nowrap">Zbl 1429.54051</a></td> </tr><tr> <td>[8]</td> <td class="space">A. LukácsandS. Kajántó,Fixed point theorems for various types ofF-contractions in completeb-metric spaces, Fixed Point Theory,19(2018), 321-334. · <a href="/1460.54047" class="nowrap">Zbl 1460.54047</a></td> </tr><tr> <td>[9]</td> <td class="space">R. Miculescu and A. Mihail,New fixed point theorems for set-valued contractions in b-metric spaces, J. Fixed Point Theory Appl.,19(3) (2017), 2153-2163. · <a href="/1383.54048" class="nowrap">Zbl 1383.54048</a></td> </tr><tr> <td>[10]</td> <td class="space">H. K. Nashine, R. P. Agarwal and Z. Kadelburg,Solution to Fredholm integral inclusions via(F, δb)-contractions, Open Mathematics,14(2016), 1053-1064. · <a href="/06675360" class="nowrap">Zbl 06675360</a></td> </tr><tr> <td>[11]</td> <td class="space">H. K. Nashine, R. P. Agarwal, S. Shukla and A. Gupta,Some fixed point theorems for almost(GF, δb)-contractions and applications, Fasciculi Math.,58(2017), 123-143. · <a href="/1369.54043" class="nowrap">Zbl 1369.54043</a></td> </tr><tr> <td>[12]</td> <td class="space">M. Nazam, M. Arshad and M. Postolache,Coincidence and common fixed point theorems for four mappings satisfying (αs, F)-contraction, Nonlinear Anal. Model. Control,23(5) (2018), 664-690. · <a href="/1420.54083" class="nowrap">Zbl 1420.54083</a></td> </tr><tr> <td>[13]</td> <td class="space">M. Nazam, Ma Zhenhua, S. U. Khan and M. Arshad,Common fixed points of four maps satisfyingF-contraction on b-metric spaces, J. Function Spaces, 2017, Art. ID 9389768, 11 pp. · <a href="/1395.54054" class="nowrap">Zbl 1395.54054</a></td> </tr><tr> <td>[14]</td> <td class="space">S. K. Padhan, G. V. V. Jagannadha Rao, A. Al-Rawashdeh, H. K. Nashine and R. P. Agarwal,Existence of fixed points forγ-F G-conractive condition via cyclic(α, β)-admissible mappings inb-metric spaces, J. Nonlinear Sci. Appl., 10(2017), 5495-5508. · <a href="/1412.47072" class="nowrap">Zbl 1412.47072</a></td> </tr><tr> <td>[15]</td> <td class="space">V. Parvaneh, N. Hussain and Z. Kadelburg,Generalized Wardowski type fixed point theorems viaα-admissibleF Gcontractions inb-metric spaces, Acta Math. Sci.,36(5) (2016), 1445-1456. · <a href="/1374.54056" class="nowrap">Zbl 1374.54056</a></td> </tr><tr> <td>[16]</td> <td class="space">H. Piri, S. Rahrovi, H. Marasi and P. Kumam,F-contraction on asymmetric metric spaces, J. Math. Comput. Sci.,17 (2017), 32-40. · <a href="/1427.54064" class="nowrap">Zbl 1427.54064</a></td> </tr><tr> <td>[17]</td> <td class="space">B. Samet, C. Vetro and P. Vetro,Fixed point theorems forα-ψ-contractive type mappings, Nonlinear Anal. TMA,75 (2012), 2154-2165. · <a href="/1242.54027" class="nowrap">Zbl 1242.54027</a></td> </tr><tr> <td>[18]</td> <td class="space">T. Suzuki,Basic inequality on ab-metric space and its applications, J. Inequal. Appl.,256(2017), 11pp. · <a href="/1377.54052" class="nowrap">Zbl 1377.54052</a></td> </tr><tr> <td>[19]</td> <td class="space">D. Wardowski,</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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