{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:25:26Z","timestamp":1760145926242,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T00:00:00Z","timestamp":1725840000000},"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>Many problems in scientific research are reduced to a nonlinear equation by mathematical means of modeling. The solutions of such equations are found mostly iteratively. Then, the convergence order is routinely shown using Taylor formulas, which in turn make sufficient assumptions about derivatives which are not present in the iterative method at hand. This technique restricts the usage of the method which may converge even if these assumptions, which are not also necessary, hold. The utilization of these methods can be extended under less restrictive conditions. This new paper contributes in this direction, since the convergence is established by assumptions restricted exclusively on the functions present on the method. Although the technique is demonstrated on a two-step Traub-type method with usually symmetric parameters and weight functions, due to its generality it can be extended to other methods defined on the real line or more abstract spaces. Numerical experimentation complement and further validate the theory.<\/jats:p>","DOI":"10.3390\/sym16091179","type":"journal-article","created":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T04:15:01Z","timestamp":1725855301000},"page":"1179","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Convergence of a Family of Methods with Symmetric, Antisymmetric Parameters and Weight Functions"],"prefix":"10.3390","volume":"16","author":[{"given":"Ramandeep","family":"Behl","sequence":"first","affiliation":[{"name":"Mathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ioannis K.","family":"Argyros","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Argyros, I.K. (2022). The Theory and Applications of Iteration Methods, CRC Press. [2nd ed.].","DOI":"10.1201\/9781003128915"},{"key":"ref_2","unstructured":"Ostrowski, A.M. (1960). Solution of Equations and System of Equations, Academic Press."},{"key":"ref_3","unstructured":"Traub, J.F. (1964). Iterative Methods for the Solution of Equations, Prentice Hall."},{"key":"ref_4","first-page":"527","article-title":"Steffensen type methods for solving non-linear equations","volume":"194","author":"Jain","year":"2007","journal-title":"Appl. Math. 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