{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:14:41Z","timestamp":1760242481908,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,8,2]],"date-time":"2017-08-02T00:00:00Z","timestamp":1501632000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The well-known Kantorovich technique based on majorizing sequences is used to analyse the convergence of Newton\u2019s method when it is used to solve nonlinear Fredholm integral equations. In addition, we obtain information about the domains of existence and uniqueness of a solution for these equations. Finally, we illustrate the above with two particular Fredholm integral equations.<\/jats:p>","DOI":"10.3390\/a10030089","type":"journal-article","created":{"date-parts":[[2017,8,2]],"date-time":"2017-08-02T10:05:25Z","timestamp":1501668325000},"page":"89","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On the Existence of Solutions of Nonlinear Fredholm Integral Equations from Kantorovich\u2019s Technique"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8120-167X","authenticated-orcid":false,"given":"Jos\u00e9","family":"Ezquerro","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computation, University of La Rioja, C\/ Madre de Dios, 53, 26006 Logro\u00f1o, Spain"}]},{"given":"Miguel","family":"Hern\u00e1ndez-Ver\u00f3n","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computation, University of La Rioja, C\/ Madre de Dios, 53, 26006 Logro\u00f1o, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2017,8,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Atkinson, K.E. 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