{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:14:29Z","timestamp":1760177669161,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,7,31]],"date-time":"2020-07-31T00:00:00Z","timestamp":1596153600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The method of discretization is used to solve nonlinear equations involving Banach space valued operators using Lipschitz or H\u00f6lder constants. But these constants cannot always be found. That is why we present results using \u03c9\u2212 continuity conditions on the Fr\u00e9chet derivative of the operator involved. This way, we extend the applicability of the discretization technique. It turns out that if we specialize \u03c9\u2212 continuity our new results improve those in the literature too in the case of Lipschitz or H\u00f6lder continuity. Our analysis includes tighter upper error bounds on the distances involved.<\/jats:p>","DOI":"10.3390\/computation8030069","type":"journal-article","created":{"date-parts":[[2020,8,3]],"date-time":"2020-08-03T03:16:46Z","timestamp":1596424606000},"page":"69","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Solution of Equations by Extended Discretization"],"prefix":"10.3390","volume":"8","author":[{"given":"Gus I.","family":"Argyros","sequence":"first","affiliation":[{"name":"Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael I.","family":"Argyros","sequence":"additional","affiliation":[{"name":"Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0035-1022","authenticated-orcid":false,"given":"Samundra","family":"Regmi","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA"}],"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\/0000-0002-3530-5539","authenticated-orcid":false,"given":"Santhosh","family":"George","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Karnataka 575025, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Amor\u00f3s, C., Argyros, I.K., Magre\u00f1\u00e1n, A.A., Regmi, S., Gonz\u00e1lez, R., and Sicilia, J.A. 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