{"id":"https://openalex.org/W1993129287","doi":"https://doi.org/10.1007/s11075-014-9952-7","title":"On the semilocal convergence of a three steps Newton-type iterative process under mild convergence conditions","display_name":"On the semilocal convergence of a three steps Newton-type iterative process under mild convergence conditions","publication_year":2015,"publication_date":"2015-01-15","ids":{"openalex":"https://openalex.org/W1993129287","doi":"https://doi.org/10.1007/s11075-014-9952-7","mag":"1993129287"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-014-9952-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-014-9952-7","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10251/67651","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033198772","display_name":"M.A. Hern\u00e1ndez","orcid":"https://orcid.org/0000-0001-5478-2958"},"institutions":[{"id":"https://openalex.org/I168974976","display_name":"Universidad de La Rioja","ror":"https://ror.org/0553yr311","country_code":"ES","type":"education","lineage":["https://openalex.org/I168974976"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"M. A. Hern\u00e1ndez-Ver\u00f3n","raw_affiliation_strings":["Department of Mathematics and Computation, University of La Rioja, 26004, Logro\u00f1o, Spain","Dept. of Mathematics and Computation, University of La Rioja, Logro\u00f1o, Spain 26004#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computation, University of La Rioja, 26004, Logro\u00f1o, Spain","institution_ids":["https://openalex.org/I168974976"]},{"raw_affiliation_string":"Dept. of Mathematics and Computation, University of La Rioja, Logro\u00f1o, Spain 26004#TAB#","institution_ids":["https://openalex.org/I168974976"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024974938","display_name":"Eulalia Mart\u0131\u0301nez","orcid":"https://orcid.org/0000-0003-2869-4334"},"institutions":[{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Eulalia Mart\u00ednez","raw_affiliation_strings":["Instituto de Matem\u00e1tica Pura y Aplicada, Universidad Polit\u00e9cnica de Valencia, Camino de Vera, s/n, 4602, Valencia, Spain","Instituto de Matem\u00e1tica Pura y Aplicada, Universidad Polit\u00e9cnica de Valencia, Valencia, Spain 4602#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica Pura y Aplicada, Universidad Polit\u00e9cnica de Valencia, Camino de Vera, s/n, 4602, Valencia, Spain","institution_ids":["https://openalex.org/I60053951"]},{"raw_affiliation_string":"Instituto de Matem\u00e1tica Pura y Aplicada, Universidad Polit\u00e9cnica de Valencia, Valencia, Spain 4602#TAB#","institution_ids":["https://openalex.org/I60053951"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024974938"],"corresponding_institution_ids":["https://openalex.org/I60053951"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":4.9132,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.95279229,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"70","issue":"2","first_page":"377","last_page":"392"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9854999780654907,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7796654105186462},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7550102472305298},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7247622013092041},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.597396194934845},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5969020128250122},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5903115272521973},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.5657715797424316},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5579690337181091},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.5578608512878418},{"id":"https://openalex.org/keywords/h\u00f6lder-condition","display_name":"H\u00f6lder condition","score":0.5260986089706421},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5241948962211609},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5150884985923767},{"id":"https://openalex.org/keywords/compact-convergence","display_name":"Compact convergence","score":0.44202202558517456},{"id":"https://openalex.org/keywords/fr\u00e9chet-derivative","display_name":"Fr\u00e9chet derivative","score":0.4273197054862976},{"id":"https://openalex.org/keywords/normal-convergence","display_name":"Normal convergence","score":0.4244692921638489},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4224141240119934},{"id":"https://openalex.org/keywords/modes-of-convergence","display_name":"Modes of convergence (annotated index)","score":0.4202570617198944},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41512852907180786},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.20161575078964233},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1770075261592865},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.16875764727592468},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1580764651298523},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1092526912689209},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.10611355304718018}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7796654105186462},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7550102472305298},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7247622013092041},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.597396194934845},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5969020128250122},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5903115272521973},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.5657715797424316},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5579690337181091},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.5578608512878418},{"id":"https://openalex.org/C553313952","wikidata":"https://www.wikidata.org/wiki/Q1537963","display_name":"H\u00f6lder condition","level":2,"score":0.5260986089706421},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5241948962211609},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5150884985923767},{"id":"https://openalex.org/C5871375","wikidata":"https://www.wikidata.org/wiki/Q1780715","display_name":"Compact convergence","level":4,"score":0.44202202558517456},{"id":"https://openalex.org/C118335899","wikidata":"https://www.wikidata.org/wiki/Q1305350","display_name":"Fr\u00e9chet derivative","level":3,"score":0.4273197054862976},{"id":"https://openalex.org/C14928880","wikidata":"https://www.wikidata.org/wiki/Q1512559","display_name":"Normal convergence","level":4,"score":0.4244692921638489},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4224141240119934},{"id":"https://openalex.org/C48216909","wikidata":"https://www.wikidata.org/wiki/Q6889156","display_name":"Modes of convergence (annotated index)","level":5,"score":0.4202570617198944},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41512852907180786},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.20161575078964233},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1770075261592865},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.16875764727592468},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1580764651298523},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1092526912689209},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.10611355304718018},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C174265945","wikidata":"https://www.wikidata.org/wiki/Q1142889","display_name":"Isolated point","level":4,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C47776270","wikidata":"https://www.wikidata.org/wiki/Q1455249","display_name":"Topological vector space","level":3,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11075-014-9952-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-014-9952-7","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:riunet.upv.es:10251/67651","is_oa":true,"landing_page_url":"http://hdl.handle.net/10251/67651","pdf_url":null,"source":{"id":"https://openalex.org/S4306400639","display_name":"RiuNet (Universitat Polit\u00e8cnica de Val\u00e8ncia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I60053951","host_organization_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","host_organization_lineage":["https://openalex.org/I60053951"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:riunet.upv.es:10251/67651","is_oa":true,"landing_page_url":"http://hdl.handle.net/10251/67651","pdf_url":null,"source":{"id":"https://openalex.org/S4306400639","display_name":"RiuNet (Universitat Polit\u00e8cnica de Val\u00e8ncia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I60053951","host_organization_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","host_organization_lineage":["https://openalex.org/I60053951"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1970633800","https://openalex.org/W1971912577","https://openalex.org/W1978739311","https://openalex.org/W2002149056","https://openalex.org/W2031937054","https://openalex.org/W2048632019","https://openalex.org/W2062432603","https://openalex.org/W2093053557","https://openalex.org/W2143608864","https://openalex.org/W3038830718","https://openalex.org/W3176239760"],"related_works":["https://openalex.org/W2034145661","https://openalex.org/W2028595206","https://openalex.org/W576291453","https://openalex.org/W2951265198","https://openalex.org/W2099365622","https://openalex.org/W2001788870","https://openalex.org/W2995787120","https://openalex.org/W2482464444","https://openalex.org/W2081461665","https://openalex.org/W2564862838"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
