{"id":"https://openalex.org/W4410721565","doi":"https://doi.org/10.3390/axioms14060401","title":"On the Convergence Order of Jarratt-Type Methods for Nonlinear Equations","display_name":"On the Convergence Order of Jarratt-Type Methods for Nonlinear Equations","publication_year":2025,"publication_date":"2025-05-24","ids":{"openalex":"https://openalex.org/W4410721565","doi":"https://doi.org/10.3390/axioms14060401"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14060401","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060401","pdf_url":"https://www.mdpi.com/2075-1680/14/6/401/pdf?version=1748070969","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/6/401/pdf?version=1748070969","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007265968","display_name":"Shobha M. Erappa","orcid":"https://orcid.org/0000-0002-6523-0873"},"institutions":[{"id":"https://openalex.org/I164861460","display_name":"Manipal Academy of Higher Education","ror":"https://ror.org/02xzytt36","country_code":"IN","type":"education","lineage":["https://openalex.org/I164861460"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Shobha M. Erappa","raw_affiliation_strings":["Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576 104, Udupi, India"],"raw_orcid":"https://orcid.org/0000-0002-6523-0873","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576 104, Udupi, India","institution_ids":["https://openalex.org/I164861460"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5117692713","display_name":"Suma P. Bheemaiah","orcid":null},"institutions":[{"id":"https://openalex.org/I164861460","display_name":"Manipal Academy of Higher Education","ror":"https://ror.org/02xzytt36","country_code":"IN","type":"education","lineage":["https://openalex.org/I164861460"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Suma P. Bheemaiah","raw_affiliation_strings":["Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576 104, Udupi, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576 104, Udupi, India","institution_ids":["https://openalex.org/I164861460"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086323665","display_name":"Santhosh George","orcid":"https://orcid.org/0000-0002-3530-5539"},"institutions":[{"id":"https://openalex.org/I11880225","display_name":"National Institute of Technology Karnataka","ror":"https://ror.org/01hz4v948","country_code":"IN","type":"education","lineage":["https://openalex.org/I11880225"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Santhosh George","raw_affiliation_strings":["Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal 575 025, Mangaluru, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal 575 025, Mangaluru, India","institution_ids":["https://openalex.org/I11880225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5117692714","display_name":"Kanagaraj Karuppaiah","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kanagaraj Karuppaiah","raw_affiliation_strings":["Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed to Be University, Kumbakonam 612 001, Tamil Nadu, India"],"raw_orcid":"https://orcid.org/0000-0002-3599-5488","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed to Be University, Kumbakonam 612 001, Tamil Nadu, India","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087674067","display_name":"Ioannis K. Argyros","orcid":"https://orcid.org/0000-0002-9189-9298"},"institutions":[{"id":"https://openalex.org/I113618177","display_name":"Cameron University","ror":"https://ror.org/00rgv0036","country_code":"US","type":"education","lineage":["https://openalex.org/I113618177"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ioannis K. Argyros","raw_affiliation_strings":["Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA","institution_ids":["https://openalex.org/I113618177"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5007265968"],"corresponding_institution_ids":["https://openalex.org/I164861460"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16262084,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"6","first_page":"401","last_page":"401"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9929999709129333,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9726999998092651,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.8175951242446899},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7890371084213257},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7084460258483887},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6977686285972595},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6169946193695068},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5705689787864685},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5680608749389648},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5623586177825928},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.5595415234565735},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.495522141456604},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3549595773220062},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3165838122367859},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31401872634887695},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.16873598098754883},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05433061718940735},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.05125635862350464}],"concepts":[{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.8175951242446899},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7890371084213257},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7084460258483887},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6977686285972595},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6169946193695068},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5705689787864685},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5680608749389648},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5623586177825928},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.5595415234565735},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.495522141456604},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3549595773220062},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3165838122367859},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31401872634887695},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.16873598098754883},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05433061718940735},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.05125635862350464},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14060401","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060401","pdf_url":"https://www.mdpi.com/2075-1680/14/6/401/pdf?version=1748070969","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:0c0265143faf40048fce8313caf191b1","is_oa":true,"landing_page_url":"https://doaj.org/article/0c0265143faf40048fce8313caf191b1","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 6, p 401 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14060401","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060401","pdf_url":"https://www.mdpi.com/2075-1680/14/6/401/pdf?version=1748070969","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410721565.pdf","grobid_xml":"https://content.openalex.org/works/W4410721565.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W562544820","https://openalex.org/W624935493","https://openalex.org/W1878535442","https://openalex.org/W1971939073","https://openalex.org/W1976890616","https://openalex.org/W1985698733","https://openalex.org/W1988627280","https://openalex.org/W1998140106","https://openalex.org/W2005999511","https://openalex.org/W2011023522","https://openalex.org/W2026376036","https://openalex.org/W2054711601","https://openalex.org/W2067572998","https://openalex.org/W2090963365","https://openalex.org/W2116996080","https://openalex.org/W2165754740","https://openalex.org/W2342862913","https://openalex.org/W2494461190","https://openalex.org/W2979792345","https://openalex.org/W3040832992","https://openalex.org/W4205246695","https://openalex.org/W4245412124","https://openalex.org/W4409117527","https://openalex.org/W6619797373","https://openalex.org/W6639162058","https://openalex.org/W6647474764","https://openalex.org/W6667258743","https://openalex.org/W6673355531","https://openalex.org/W6684473933","https://openalex.org/W7019992027"],"related_works":["https://openalex.org/W2395105737","https://openalex.org/W2369507325","https://openalex.org/W3208270790","https://openalex.org/W3135719690","https://openalex.org/W2368550193","https://openalex.org/W1985023705","https://openalex.org/W2340858455","https://openalex.org/W2109499508","https://openalex.org/W3040537092","https://openalex.org/W2527460344"],"abstract_inverted_index":{"The":[0,38,73],"order":[1,61],"of":[2,29,46,59,62,70,82,102],"convergence":[3,87],"for":[4,55,104],"Jarratt-type":[5],"methods":[6],"in":[7,41,85,92],"solving":[8],"nonlinear":[9],"equations":[10],"is":[11,44,76],"determined":[12],"without":[13],"relying":[14],"on":[15,24],"Taylor":[16,48],"expansion.":[17],"Unlike":[18],"previous":[19],"studies,":[20],"we":[21],"depend":[22],"solely":[23],"assumptions":[25,56],"about":[26,57],"the":[27,30,35,47,53,63,68,80,105],"derivatives":[28,58],"involved":[31,64],"operator":[32,65],"up":[33],"to":[34],"second":[36],"order.":[37],"proof":[39],"presented":[40],"this":[42],"paper":[43],"independent":[45],"series":[49],"expansion,":[50],"thereby":[51],"reducing":[52],"need":[54],"higher":[60],"and":[66,89,100],"enhancing":[67],"applicability":[69,75],"these":[71],"methods.":[72,106],"method\u2019s":[74],"broadened":[77],"by":[78],"employing":[79],"concept":[81],"generalized":[83],"conditions":[84],"local":[86],"analysis":[88],"majorizing":[90],"sequences":[91],"semi-local":[93],"analysis.":[94],"This":[95],"study":[96],"includes":[97],"numerical":[98],"examples":[99],"basins":[101],"attraction":[103]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
