Document Zbl 1142.47033

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Math. Anal. Appl.</a> <a href="/?q=in%3A217451" title="Articles in this Issue">341, No. 2, 1241-1252 (2008)</a>. </div> <div class="abstract">The authors present some fixed point results for self-generalized contractions in ordered metric spaces. These results generalize some recent results of <span class="zbmathjax-textit">A. C. M. Ran</span> and <span class="zbmathjax-textit">M. C. Reurings</span> [Proc. Am. Math. Soc. 132, No. 5, 1435–1443 (2004; <a href="/1060.47056">Zbl 1060.47056</a>)] as well as <span class="zbmathjax-textit">J. J. Nieto</span> and <span class="zbmathjax-textit">R. Rodríguez-Lopez</span> [Order 22, No. 3, 223–239 (2005; <a href="/1095.47013">Zbl 1095.47013</a>); Acta Math. Sin. Engl. Ser. 23, 2205–2212 (2007; <a href="/1140.47045">Zbl 1140.47045</a>)], in terms of Picard operators [cf. <span class="zbmathjax-textit">I. A. Rus</span>, Sci. Math. Jpn. 58, No. 1, 191–219 (2003; <a href="/1031.47035">Zbl 1031.47035</a>)]. Moreover, for the case of generalized $\varphi$-contractions, a fixed point theorem is established, as a modification of that of <span class="zbmathjax-textit">R. P. Agarwal, M. A. El–Gebeily</span>, and <span class="zbmathjax-textit">D. O’Regan</span> [Appl. Anal. 87, No. 1, 109–116 (2008; <a href="/1140.47042">Zbl 1140.47042</a>)]. Some applications are given to Fredholm and Volterra type integral equations.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A11147">In-Sook Kim (München)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A5255948">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A5255948">Cited in <strong>201</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A47H10" title="MSC2020">47H10</a> </td> <td class="space"> Fixed-point theorems </td> </tr><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%3A47H07" title="MSC2020">47H07</a> </td> <td class="space"> Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A47H09" title="MSC2020">47H09</a> </td> <td class="space"> Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc. </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Afixed+point">fixed point</a>; <a href="/?q=ut%3Amonotone+operator">monotone operator</a>; <a href="/?q=ut%3Aordered+metric+space">ordered metric space</a>; <a href="/?q=ut%3Ageneralised+contraction">generalised contraction</a>; <a href="/?q=ut%3AFredholm+integral+equations">Fredholm integral equations</a>; <a href="/?q=ut%3AVolterra-type+integral+equations">Volterra-type integral equations</a></div><div class="keywords"> <h3>Citations:</h3><a href="/1060.47056">Zbl 1060.47056</a>; <a href="/1095.47013">Zbl 1095.47013</a>; <a href="/1031.47035">Zbl 1031.47035</a>; <a href="/1140.47045">Zbl 1140.47045</a>; <a href="/1140.47042">Zbl 1140.47042</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 1142.47033" data-ciurl="/ci/05255948" data-biburl="/bibtex/05255948.bib" data-amsurl="/amsrefs/05255948.bib" data-xmlurl="/xml/05255948.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05255948.pdf" title="Zbl 1142.47033 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/10.1016/j.jmaa.2007.11.026" aria-label="DOI for “Fixed point theorems for generalized contractions in ordered metric spaces”" title="10.1016/j.jmaa.2007.11.026">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">R.P. Agarwal, M.A. El-Gebeily, D. O’Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., in press; R.P. Agarwal, M.A. El-Gebeily, D. O’Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., in press · <a href="/1140.47042" class="nowrap">Zbl 1140.47042</a></td> </tr><tr> <td>[2]</td> <td class="space">Drici, Z.; McRae, F. A.; Vasundhara Devi, J., Fixed point theorems in partially ordered metric spaces for operators with PPF dependence, Nonlinear Anal., 7, 641-647 (2007) · <a href="/1127.47049" class="nowrap">Zbl 1127.47049</a></td> </tr><tr> <td>[3]</td> <td class="space">Fréchet, M., Les espaces abstraits (1928), Gauthier-Villars: Gauthier-Villars Paris · <a href="/54.0614.02" class="nowrap">JFM 54.0614.02</a></td> </tr><tr> <td>[4]</td> <td class="space">Hadžić, O.; Pap, E.; Radu, V., Generalized contraction mapping principles in probabilistic metric spaces, Acta Math. Hungar., 101, 131-138 (2003) · <a href="/1050.47052" class="nowrap">Zbl 1050.47052</a></td> </tr><tr> <td>[5]</td> <td class="space">Hadžić, O.; Pap, E., Fixed Point Theory in Probabilistic Metric Spaces (2001), Kluwer Acad. Publ.: Kluwer Acad. Publ. Dordrecht</td> </tr><tr> <td>[6]</td> <td class="space">Jachymski, J.; Jóźwik, I., Nonlinear contractive conditions: A comparison and related problems, Banach Center Publ., 77, 123-146 (2007) · <a href="/1149.47044" class="nowrap">Zbl 1149.47044</a></td> </tr><tr> <td>[7]</td> <td class="space">Nieto, J. J.; Rodríguez-López, R., Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22, 223-239 (2005) · <a href="/1095.47013" class="nowrap">Zbl 1095.47013</a></td> </tr><tr> <td>[8]</td> <td class="space">Nieto, J. J.; Pouso, R. L.; Rodríguez-López, R., Fixed point theorem theorems in ordered abstract sets, Proc. Amer. Math. Soc., 135, 2505-2517 (2007) · <a href="/1126.47045" class="nowrap">Zbl 1126.47045</a></td> </tr><tr> <td>[9]</td> <td class="space">Nieto, J. J.; Rodríguez-López, R., Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.), 23, 2205-2212 (2007) · <a href="/1140.47045" class="nowrap">Zbl 1140.47045</a></td> </tr><tr> <td>[10]</td> <td class="space">Petruşel, A.; Rus, I. A., Fixed point theorems in ordered $L$-spaces, Proc. Amer. Math. Soc., 134, 411-418 (2006) · <a href="/1086.47026" class="nowrap">Zbl 1086.47026</a></td> </tr><tr> <td>[11]</td> <td class="space">Ran, A. C.M.; Reurings, M. C., A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132, 1435-1443 (2004) · <a href="/1060.47056" class="nowrap">Zbl 1060.47056</a></td> </tr><tr> <td>[12]</td> <td class="space">Rus, I. A., Generalized Contractions and Applications (2001), Cluj Univ. Press · <a href="/0968.54029" class="nowrap">Zbl 0968.54029</a></td> </tr><tr> <td>[13]</td> <td class="space">Rus, I. A., Picard operators and applications, Sci. Math. Jpn., 58, 191-219 (2003) · <a href="/1031.47035" class="nowrap">Zbl 1031.47035</a></td> </tr><tr> <td>[14]</td> <td class="space">Rus, I. A.; Petruşel, A.; Petruşel, G., Fixed Point Theory 1950-2000: Romanian Contributions (2002), House of the Book of Science: House of the Book of Science Cluj-Napoca · <a href="/1005.54037" class="nowrap">Zbl 1005.54037</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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