Document Zbl 1393.47027

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(2016)</a>. </div> <div class="abstract">Summary: In this paper, a new modified proximal point algorithm involving fixed point iterates of asymptotically nonexpansive mappings in $\operatorname {CAT}(0)$ spaces is proposed and the existence of a sequence generated by our iterative process converging to a minimizer of a convex function and a common fixed point of asymptotically nonexpansive mappings is proved.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6610391">Cited in <strong>20</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%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%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%3Aconvex+minimization+problem">convex minimization problem</a>; <a href="/?q=ut%3Aresolvent+identity">resolvent identity</a>; <a href="/?q=ut%3A%5C%28%5Coperatorname%7BCAT%7D%280%29%5C%29+space">$\operatorname{CAT}(0)$ space</a>; <a href="/?q=ut%3Aproximal+point+algorithm">proximal point algorithm</a>; <a href="/?q=ut%3Aasymptotically+nonexpansive+mapping">asymptotically nonexpansive mapping</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 1393.47027" data-ciurl="/ci/06610391" data-biburl="/bibtex/06610391.bib" data-amsurl="/amsrefs/06610391.bib" data-xmlurl="/xml/06610391.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06610391.pdf" title="Zbl 1393.47027 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/10.1186/s13663-016-0559-7" aria-label="DOI for “Some convergence theorems involving proximal point and common fixed points for asymptotically nonexpansive mappings in $\operatorname {CAT}(0)$ spaces”" title="10.1186/s13663-016-0559-7">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">Martinet, B: Réularisation d’inéquations variationnelles par approximations successives. 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