{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T21:26:49Z","timestamp":1767907609070,"version":"3.49.0"},"reference-count":15,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,11,24]],"date-time":"2022-11-24T00:00:00Z","timestamp":1669248000000},"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>Symmetries play a vital role in the study of physical systems. For example, microworld and quantum physics problems are modeled on the principles of symmetry. These problems are then formulated as equations defined on suitable abstract spaces. Most of these studies reduce to solving nonlinear equations in suitable abstract spaces iteratively. In particular, the convergence of a sixth-order Cordero type iterative method for solving nonlinear equations was studied using Taylor expansion and assumptions on the derivatives of order up to six. In this study, we obtained order of convergence six for Cordero type method using assumptions only on the first derivative. Moreover, we modified Cordero\u2019s method and obtained an eighth-order iterative scheme. Further, we considered analogous iterative methods to solve an ill-posed problem in a Hilbert space setting.<\/jats:p>","DOI":"10.3390\/sym14122495","type":"journal-article","created":{"date-parts":[[2022,11,25]],"date-time":"2022-11-25T02:29:23Z","timestamp":1669343363000},"page":"2495","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Extending the Applicability of Cordero Type Iterative Method"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6713-8483","authenticated-orcid":false,"given":"Krishnendu","family":"Remesh","sequence":"first","affiliation":[{"name":"Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore 575 025, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9189-9298","authenticated-orcid":false,"given":"Ioannis K.","family":"Argyros","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6628-3136","authenticated-orcid":false,"given":"Muhammed","family":"Saeed K","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore 575 025, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3530-5539","authenticated-orcid":false,"given":"Santhosh","family":"George","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore 575 025, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9448-1906","authenticated-orcid":false,"given":"Jidesh","family":"Padikkal","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore 575 025, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2369","DOI":"10.1016\/j.aml.2012.07.005","article-title":"Increasing the convergence order of an iterative method for nonlinear systems","volume":"25","author":"Cordero","year":"2012","journal-title":"Appl. Math. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1016\/j.cam.2009.04.015","article-title":"Iterative methods of order four and five for systems of nonlinear equations","volume":"231","author":"Cordero","year":"2012","journal-title":"J. Comput. Appl. Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/s11075-009-9359-z","article-title":"A modified Newton Jarratt\u2019s composition","volume":"55","author":"Cordero","year":"2010","journal-title":"Numer. Algor."},{"key":"ref_4","first-page":"396","article-title":"On the local convergence of a fifth-order iterative method in Banach spaces","volume":"251","author":"Cordero","year":"2012","journal-title":"Appl. Math. Comput."},{"key":"ref_5","first-page":"269","article-title":"An efficient newton-type method with fifthorder convergence for solving nonlinear equations","volume":"227","author":"Fang","year":"2008","journal-title":"Comput. Appl. Math."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1016\/j.cam.2011.08.008","article-title":"On the computational efficiency index and some iterative methods for solving systems of nonlinear equations","volume":"236","author":"Grau","year":"2021","journal-title":"J. Comput. Appl. Math."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1016\/j.camwa.2013.12.004","article-title":"An efficient fifth order method for solving systems of nonlinear equations","volume":"67","author":"Sharma","year":"2014","journal-title":"Comput. Math. Appl."},{"key":"ref_8","first-page":"520","article-title":"A novel family of composite Newton\u2013Traub methods for solving systems of nonlinear equations","volume":"269","author":"Sharma","year":"2015","journal-title":"Appl. Math. Comput."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Parhi, S.K., and Sharma, D. (2021). On the Local Convergence of a Sixth-Order Iterative Scheme in Banach Spaces. New Trends in Applied Analysis and Computational Mathematics, Springer.","DOI":"10.1007\/978-981-16-1402-6_7"},{"key":"ref_10","unstructured":"Argyros, I.K. (2022). The Theory and Applications of Iteration Methods, CRC Press, Taylor and Francis Group. [2nd ed.]. Engineering Series."},{"key":"ref_11","unstructured":"Ostrowski, A.M. (1973). Solution of Equations in Euclidean and Banach Spaces, Elsevier."},{"key":"ref_12","unstructured":"Traub, J.F. (1964). Iterative Methods for Solution of Equations, Prentice-Hal."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"George, S., Saeed, M., Argyros, I.K., and Jidesh, P. (2022). An apriori parameter choice strategy and a fifth order iterative scheme for Lavrentiev regularization method. J. Appl. Math. Comput., 1\u201321.","DOI":"10.1007\/s12190-022-01782-3"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"George, S., Jidesh, P., Krishnendu, R., and Argyros, I.K. (2022). A new parameter choice strategy for Lavrentiev regularization method for nonlinear ill-posed equations. Mathematics, 10.","DOI":"10.3390\/math10183365"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1140","DOI":"10.1080\/01630560802484294","article-title":"Regularized versions of continuous Newton\u2019s method and continuous modified Newton\u2019s method under general source conditions","volume":"29","author":"Nair","year":"2008","journal-title":"Numer. Funct. Anal. Optim."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/12\/2495\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:26:19Z","timestamp":1760145979000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/12\/2495"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,24]]},"references-count":15,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["sym14122495"],"URL":"https:\/\/doi.org\/10.3390\/sym14122495","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,24]]}}}