{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T06:05:37Z","timestamp":1778133937091,"version":"3.51.4"},"reference-count":14,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,1,23]],"date-time":"2019-01-23T00:00:00Z","timestamp":1548201600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper we present a two-step solver for nonlinear equations with a nondifferentiable operator. This method is based on two methods of order of convergence     1 +  2     . We study the local and a semilocal convergence using weaker conditions in order to extend the applicability of the solver. Finally, we present the numerical example that confirms the theoretical results.<\/jats:p>","DOI":"10.3390\/sym11020128","type":"journal-article","created":{"date-parts":[[2019,1,24]],"date-time":"2019-01-24T03:52:32Z","timestamp":1548301952000},"page":"128","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Two-Step Solver for Nonlinear Equations"],"prefix":"10.3390","volume":"11","author":[{"given":"Ioannis K.","family":"Argyros","sequence":"first","affiliation":[{"name":"Department of Mathematics, Cameron University, Lawton, OK 73505, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3845-6260","authenticated-orcid":false,"given":"Stepan","family":"Shakhno","sequence":"additional","affiliation":[{"name":"Faculty of Applied Mathematics and Informatics, Ivan Franko National University of Lviv, Universitetska Str. 1, Lviv 79000, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Halyna","family":"Yarmola","sequence":"additional","affiliation":[{"name":"Faculty of Applied Mathematics and Informatics, Ivan Franko National University of Lviv, Universitetska Str. 1, Lviv 79000, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1016\/j.jmaa.2004.04.008","article-title":"A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space","volume":"298","author":"Argyros","year":"2004","journal-title":"J. Math. Anal. Appl."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Argyros, I.K., and Magren\u00e1n, \u00c1.A. (2017). Iterative Methods and Their Dynamics with Applications: A Contemporary Study, CRC Press.","DOI":"10.1201\/9781315153469"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1016\/j.cam.2009.05.010","article-title":"On the convergence of modified Newton methods for solving equations containing a non-differentiable term","volume":"231","author":"Argyros","year":"2009","journal-title":"J. Comp. App. Math."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1016\/S0022-247X(02)00432-8","article-title":"A uniparametric family of iterative processes for solving nondiffrentiable operators","volume":"275","author":"Hernandez","year":"2002","journal-title":"J. Math. Anal. 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