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Dyn. Differ. Equations</a> <a href="/?q=in%3A364659" title="Articles in this Issue">29, No. 1, 155-168 (2017)</a>. </div> <div class="abstract">This interesting and well-written paper is devoted to a detailed study of certain non-autonomous first-order initial value problems governed by a nonexpansive operator \(T\) with fixed points defined on a real Hilbert space. The authors first establish the existence and uniqueness of absolutely continuous solutions and then they prove that all trajectories weakly converge to a fixed point of \(T\). They also present applications for solving monotone inclusions and discuss discrete-time analogues. Finally, time-rescaling techniques are used to provide an alternative approach in which some results are deduced from the convergence behavior of an autonomous dynamical system described by <span class="zbmathjax-textit">B. Abbas</span> and <span class="zbmathjax-textit">H. Attouch</span> [Optimization 64, No. 10, 2223&ndash;2252 (2015; <a href="/1345.34115">Zbl&nbsp;1345.34115</a>)]. In this connection, see also the early papers by <span class="zbmathjax-textit">R. E. Bruck</span> and the reviewer [Houston J. Math. 3, 459&ndash;470 (1977; <a href="/0383.47035">Zbl&nbsp;0383.47035</a>)], and by <span class="zbmathjax-textit">J. B. Baillon</span> et al. [Houston J. Math. 4, 1&ndash;9 (1978; <a href="/0396.47033">Zbl&nbsp;0396.47033</a>); ibid. 4, 1&ndash;9 (1978; <a href="/0431.47034">Zbl&nbsp;0431.47034</a>)].<div class="reviewer"> Reviewer:&nbsp;<a href="/authors/?q=rv%3A2181">Simeon Reich (Haifa)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6706444">Cited in <strong>37</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A34G25" title="MSC2020">34G25</a> </td> <td class="space"> Evolution inclusions </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34G20" title="MSC2020">34G20</a> </td> <td class="space"> Nonlinear differential equations in abstract spaces </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A47J25" title="MSC2020">47J25</a> </td> <td class="space"> Iterative procedures involving nonlinear operators </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A47H05" title="MSC2020">47H05</a> </td> <td class="space"> Monotone operators and generalizations </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><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C25" title="MSC2020">90C25</a> </td> <td class="space"> Convex programming </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34D05" title="MSC2020">34D05</a> </td> <td class="space"> Asymptotic properties of solutions to ordinary differential equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Adynamical+systems">dynamical systems</a>; <a href="/?q=ut%3ALyapunov+analysis">Lyapunov analysis</a>; <a href="/?q=ut%3AKrasnosel%27ski%C4%AD-Mann+algorithm">Krasnosel&rsquo;skiĭ-Mann algorithm</a>; <a href="/?q=ut%3Amonotone+inclusions">monotone inclusions</a>; <a href="/?q=ut%3Aforward-backward+algorithm">forward-backward algorithm</a></div><div class="keywords"> <h3>Citations:</h3><a href="/1345.34115">Zbl 1345.34115</a>; <a href="/0383.47035">Zbl 0383.47035</a>; <a href="/0396.47033">Zbl 0396.47033</a>; <a href="/0431.47034">Zbl 0431.47034</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <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">&times;</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;"> <!-- alert for connection errors etc --> </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"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1387.34091" data-ciurl="/ci/06706444" data-biburl="/bibtex/06706444.bib" data-amsurl="/amsrefs/06706444.bib" data-xmlurl="/xml/06706444.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06706444.pdf" title="Zbl 1387.34091 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/10.1007/s10884-015-9438-x" aria-label="DOI for “A dynamical system associated with the fixed points set of a nonexpansive operator”" title="10.1007/s10884-015-9438-x">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1411.4442"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Abbas, B., Attouch, H.: Dynamical systems and forward-backward algorithms associated with the sum of a convex subdifferential and a monotone cocoercive operator. 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North-Holland/Elsevier, New York (1973) &middot; <a href="/0252.47055" class="nowrap">Zbl 0252.47055</a></td> </tr><tr> <td>[13]</td> <td class="space">Briceño-Arias, L.M.: Forward-Douglas-Rachford splitting and forward-partial inverse method for solving monotone inclusions. Optimization (2013). doi:10.1080/02331934.2013.855210 &middot; <a href="/1310.47084" class="nowrap">Zbl 1310.47084</a></td> </tr><tr> <td>[14]</td> <td class="space">Bruck Jr, R.E.: Asymptotic convergence of nonlinear contraction semigroups in Hilbert space. J. Funct. Anal. 18, 15-26 (1975) &middot; <a href="/0319.47041" class="nowrap">Zbl 0319.47041</a>&nbsp;&middot; <a href="https://doi.org/10.1016/0022-1236(75)90027-0" class="nowrap">doi:10.1016/0022-1236(75)90027-0</a></td> </tr><tr> <td>[15]</td> <td class="space">Corman, E., Yuan, X.: A Generalized proximal point algorithm and its convergence rate. SIAM J. 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