{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:40:08Z","timestamp":1760240408990,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,6,6]],"date-time":"2019-06-06T00:00:00Z","timestamp":1559779200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003359","name":"Generalitat Valenciana","doi-asserted-by":"publisher","award":["PROMETEO2016\/089"],"award-info":[{"award-number":["PROMETEO2016\/089"]}],"id":[{"id":"10.13039\/501100003359","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["PGC2018-095896-B-C22"],"award-info":[{"award-number":["PGC2018-095896-B-C22"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this manuscript, by using the weight-function technique, a new class of iterative methods for solving nonlinear problems is constructed, which includes many known schemes that can be obtained by choosing different weight functions. This weight function, depending on two different evaluations of the derivative, is the unique difference between the two steps of each method, which is unusual. As it is proven that all the members of the class are optimal methods in the sense of Kung-Traub\u2019s conjecture, the dynamical analysis is a good tool to determine the best elements of the family in terms of stability. Therefore, the dynamical behavior of this class on quadratic polynomials is studied in this work. We analyze the stability of the presented family from the multipliers of the fixed points and critical points, along with their associated parameter planes. In addition, this study enables us to select the members of the class with good stability properties.<\/jats:p>","DOI":"10.3390\/sym11060769","type":"journal-article","created":{"date-parts":[[2019,6,7]],"date-time":"2019-06-07T03:56:31Z","timestamp":1559879791000},"page":"769","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Fixed Point Root-Finding Methods of Fourth-Order of Convergence"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7462-9173","authenticated-orcid":false,"given":"Alicia","family":"Cordero","sequence":"first","affiliation":[{"name":"Instituto Universitario de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s\/n, 46022 Val\u00e8ncia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luc\u00eda","family":"Guasp","sequence":"additional","affiliation":[{"name":"Instituto Universitario de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s\/n, 46022 Val\u00e8ncia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9893-0761","authenticated-orcid":false,"given":"Juan R.","family":"Torregrosa","sequence":"additional","affiliation":[{"name":"Instituto Universitario de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s\/n, 46022 Val\u00e8ncia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Petkovi\u0107, M., Neta, B., Petkovi\u0107, L.D., and D\u017euni\u0107, J. (2013). Multipoint Methods for Solving Nonlinear Equations, Academic Press.","DOI":"10.1016\/B978-0-12-397013-8.00002-9"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Amat, S., and Busquier, S. (2016). Advances in Iterative Methods for Nonlinear Equations, Springer SIMAI.","DOI":"10.1007\/978-3-319-39228-8"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.cad.2017.05.023","article-title":"Solving piecewise polynomial constraint systems with decomposition and a subdivision-based solver","volume":"90","author":"Elber","year":"2017","journal-title":"Comput.-Aided Des."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1145\/321850.321860","article-title":"Optimal order of one-point and multipoint iteration","volume":"21","author":"Kung","year":"1974","journal-title":"J. Assoc. Comput. 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Math."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"415","DOI":"10.3390\/a8030415","article-title":"A Quartically convergent Jarratt-type method for solving systems of equations","volume":"8","author":"Ghorbanzadeh","year":"2015","journal-title":"Algorithms"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1090\/S0273-0979-1984-15240-6","article-title":"Complex Analytic Dynamics on the Riemann Sphere","volume":"11","author":"Blanchard","year":"1984","journal-title":"Bull. AMS"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1090\/psapm\/049\/1315536","article-title":"The Dynamics of Newton\u2019s Method","volume":"49","author":"Blanchard","year":"1994","journal-title":"Proc. Symp. Appl. 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World J."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/6\/769\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:56:40Z","timestamp":1760187400000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/6\/769"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,6]]},"references-count":14,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2019,6]]}},"alternative-id":["sym11060769"],"URL":"https:\/\/doi.org\/10.3390\/sym11060769","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,6,6]]}}}