{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T14:42:40Z","timestamp":1760452960354,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,5,25]],"date-time":"2019-05-25T00:00:00Z","timestamp":1558742400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Numerous higher-order methods with derivative evaluations are accessible in the literature for computing multiple zeros. However, higher-order methods without derivatives are very rare for multiple zeros. Encouraged by this fact, we present a family of third-order derivative-free iterative methods for multiple zeros that require only evaluations of three functions per iteration. Convergence of the proposed class is demonstrated by means of using a graphical tool, namely basins of attraction. Applicability of the methods is demonstrated through numerical experimentation on different functions that illustrates the efficient behavior. Comparison of numerical results shows that the presented iterative methods are good competitors to the existing techniques.<\/jats:p>","DOI":"10.3390\/axioms8020065","type":"journal-article","created":{"date-parts":[[2019,5,26]],"date-time":"2019-05-26T23:07:27Z","timestamp":1558912047000},"page":"65","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["An Efficient Class of Traub\u2013Steffensen-Type Methods for Computing Multiple Zeros"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3500-3087","authenticated-orcid":false,"given":"Deepak","family":"Kumar","sequence":"first","affiliation":[{"name":"Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal 148106, Sangrur, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4627-2795","authenticated-orcid":false,"given":"Janak Raj","family":"Sharma","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal 148106, Sangrur, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Clemente","family":"Cesarano","sequence":"additional","affiliation":[{"name":"Section of Mathematics, International Telematic University UNINETTUNO, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/BF01444024","article-title":"\u00dcber unendlich viele Algorithmen zur Aufl\u00f6sung der Gleichungen","volume":"2","year":"1870","journal-title":"Math. 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