Document Zbl 1439.30023

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Commun.</a> <a href="/?q=in%3A449225" title="Articles in this Issue">25, No. 1, 117-135 (2020)</a>. </div> <div class="abstract">Summary: In this paper our aim is to find the radii of starlikeness and convexity of the generalized Mittag-Leffler function for three different kinds of normalization by using their Hadamard factorization in such a way that the resulting functions are analytic in the unit disk of the complex plane. The characterization of entire functions from Laguerre-P贸lya class and a result of H. Kumar and M.A. Pathan on the reality of the zeros of generalized Mittag-Leffler functions, which origins goes back to Dzhrbashyan, Ostrovski沫 and Peresyolkova, play important roles in this paper. Moreover, the interlacing properties of the zeros of Mittag-Leffler function and its derivative is also useful in the proof of the main results. By using the Euler-Rayleigh inequalities for the real zeros of the generalized Mittag-Leffler function, we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7200859">Cited in <strong>7</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A30C45" title="MSC2020">30C45</a> </td> <td class="space"> Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A30C15" title="MSC2020">30C15</a> </td> <td class="space"> Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A33E12" title="MSC2020">33E12</a> </td> <td class="space"> Mittag-Leffler functions and generalizations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ageneralized+Mittag-Leffler+functions">generalized Mittag-Leffler functions</a>; <a href="/?q=ut%3Astar-like+functions">star-like functions</a>; <a href="/?q=ut%3Aconvex+functions">convex functions</a>; <a href="/?q=ut%3Aradius+of+star-likeness">radius of star-likeness</a>; <a href="/?q=ut%3Aradius+of+convexity">radius of convexity</a></div> <div class="software"> <h3>Software:</h3><a href="/software/20907">ML</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 1439.30023" data-ciurl="/ci/07200859" data-biburl="/bibtex/07200859.bib" data-amsurl="/amsrefs/07200859.bib" data-xmlurl="/xml/07200859.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07200859.pdf" title="Zbl 1439.30023 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://arxiv.org/abs/1901.04333"title="Note: arXiv document may differ from published version">arXiv</a> <a class="btn btn-default btn-xs" type="button" href="https://hrcak.srce.hr/235561" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">I. 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