Document Zbl 1520.47008

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Malays. Math. Sci. Soc. (2)</a> <a href="/?q=in%3A454895" title="Articles in this Issue">43, No. 6, 3963-4005 (2020)</a>. </div> <div class="abstract">Summary: The main aim of this paper is to consider various notions of (dense) $m_n$-distributional chaos of type $s$ and (dense) reiterative $m_n$-distributional chaos of type $s$ for general sequences of linear not necessarily continuous operators in Fréchet spaces. Here, $(m_n)$ is an increasing sequence in $[1,\infty)$ satisfying $\liminf_{n\rightarrow \infty}\frac{m_n}{n}>0$ and $s$ could be $0,1,2,2+,2\frac{1}{2},3,1+,2-,2_{Bd},2_{Bd}+$. We investigate $m_n $-distributionally chaotic properties and reiteratively $m_n$-distributionally chaotic properties of some special classes of operators like weighted forward shift operators and weighted backward shift operators in Fréchet sequence spaces, considering also continuous analogues of introduced notions and some applications to abstract partial differential equations.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7270602">Cited in <strong>3</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A47A06" title="MSC2020">47A06</a> </td> <td class="space"> Linear relations (multivalued linear operators) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A47A16" title="MSC2020">47A16</a> </td> <td class="space"> Cyclic vectors, hypercyclic and chaotic operators </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3A%5C%28m_n%5C%29-distributional+chaos+of+type+%5C%28s%5C%29">$m_n$-distributional chaos of type $s$</a>; <a href="/?q=ut%3Areiterative+%5C%28m_n%5C%29-distributional+chaos+of+type+%5C%28s%5C%29">reiterative $m_n$-distributional chaos of type $s$</a>; <a href="/?q=ut%3A%5C%28%5Clambda+%5C%29-distributional+chaos+of+type+%5C%28s%5C%29">$\lambda $-distributional chaos of type $s$</a>; <a href="/?q=ut%3Areiterative+%5C%28%5Clambda+%5C%29-distributional+chaos+of+type+%5C%28s%5C%29">reiterative $\lambda $-distributional chaos of type $s$</a>; <a href="/?q=ut%3AFr%C3%A9chet+spaces">Fréchet spaces</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 1520.47008" data-ciurl="/ci/07270602" data-biburl="/bibtex/07270602.bib" data-amsurl="/amsrefs/07270602.bib" data-xmlurl="/xml/07270602.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07270602.pdf" title="Zbl 1520.47008 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/s40840-020-00906-x" aria-label="DOI for “Reiterative $m_n$-distributional chaos of type $s$ in Fréchet spaces”" title="10.1007/s40840-020-00906-x">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1902.03474"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">Barrachina, X.; Conejero, JA, Devaney chaos and distributional chaos in the solution of certain partial differential equations, Abstr. 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