{"id":"https://openalex.org/W1687769292","doi":"https://doi.org/10.3390/a8040832","title":"Newton-Type Methods on Generalized Banach Spaces and Applications in Fractional Calculus","display_name":"Newton-Type Methods on Generalized Banach Spaces and Applications in Fractional Calculus","publication_year":2015,"publication_date":"2015-10-09","ids":{"openalex":"https://openalex.org/W1687769292","doi":"https://doi.org/10.3390/a8040832","mag":"1687769292"},"language":"en","primary_location":{"id":"doi:10.3390/a8040832","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a8040832","pdf_url":"https://www.mdpi.com/1999-4893/8/4/832/pdf?version=1445309680","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/8/4/832/pdf?version=1445309680","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015220542","display_name":"George A. Anastassiou","orcid":"https://orcid.org/0000-0002-3781-9824"},"institutions":[{"id":"https://openalex.org/I94658018","display_name":"University of Memphis","ror":"https://ror.org/01cq23130","country_code":"US","type":"education","lineage":["https://openalex.org/I94658018"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"George Anastassiou","raw_affiliation_strings":["Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA","institution_ids":["https://openalex.org/I94658018"]}]},{"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":true,"raw_author_name":"Ioannis Argyros","raw_affiliation_strings":["Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA"],"raw_orcid":"https://orcid.org/0000-0002-9189-9298","affiliations":[{"raw_affiliation_string":"Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA","institution_ids":["https://openalex.org/I113618177"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087674067"],"corresponding_institution_ids":["https://openalex.org/I113618177"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.503,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.63144481,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"8","issue":"4","first_page":"832","last_page":"849"},"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":0.9995999932289124,"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":0.9860000014305115,"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/fractional-calculus","display_name":"Fractional calculus","score":0.8515496253967285},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.759014904499054},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6267312169075012},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.6181919574737549},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6104507446289062},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.608802318572998},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5728137493133545},{"id":"https://openalex.org/keywords/fr\u00e9chet-derivative","display_name":"Fr\u00e9chet derivative","score":0.5412350296974182},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.46529969573020935},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44722428917884827},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35903793573379517}],"concepts":[{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.8515496253967285},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.759014904499054},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6267312169075012},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.6181919574737549},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6104507446289062},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.608802318572998},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5728137493133545},{"id":"https://openalex.org/C118335899","wikidata":"https://www.wikidata.org/wiki/Q1305350","display_name":"Fr\u00e9chet derivative","level":3,"score":0.5412350296974182},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.46529969573020935},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44722428917884827},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35903793573379517},{"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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":3,"locations":[{"id":"doi:10.3390/a8040832","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a8040832","pdf_url":"https://www.mdpi.com/1999-4893/8/4/832/pdf?version=1445309680","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:eb3d0eed89334b8ebf04200f85d6d283","is_oa":false,"landing_page_url":"https://doaj.org/article/eb3d0eed89334b8ebf04200f85d6d283","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 8, Iss 4, Pp 832-849 (2015)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/8/4/832/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/a8040832","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a8040832","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a8040832","pdf_url":"https://www.mdpi.com/1999-4893/8/4/832/pdf?version=1445309680","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W186843137","https://openalex.org/W232674853","https://openalex.org/W561050696","https://openalex.org/W1528063838","https://openalex.org/W1555232731","https://openalex.org/W1971939073","https://openalex.org/W1975670568","https://openalex.org/W1995094333","https://openalex.org/W2022703159","https://openalex.org/W2047475327","https://openalex.org/W2073351385","https://openalex.org/W2104500275","https://openalex.org/W2149757112","https://openalex.org/W4247953052","https://openalex.org/W6682291009"],"related_works":["https://openalex.org/W2245126542","https://openalex.org/W2969585421","https://openalex.org/W1989433389","https://openalex.org/W1996428104","https://openalex.org/W2097846334","https://openalex.org/W2021009798","https://openalex.org/W2547159309","https://openalex.org/W2314912066","https://openalex.org/W4247076037","https://openalex.org/W4296052657"],"abstract_inverted_index":{"We":[0],"present":[1,36],"a":[2,10,17],"semilocal":[3],"convergence":[4,75,104],"study":[5,37],"of":[6,21,52,94,117],"Newton-type":[7,53],"methods":[8,54],"on":[9,80,91],"generalized":[11],"Banach":[12],"space":[13],"setting":[14],"to":[15,55,114],"approximate":[16],"locally":[18],"unique":[19],"zero":[20],"an":[22,85],"operator.":[23],"Earlier":[24],"studies":[25],"require":[26],"that":[27,40],"the":[28,35,41,50,66,81,92,95,102,109,125,130],"operator":[29,42],"involved":[30,83],"is":[31,43,136],"Fr\u00e9chet":[32],"differentiable.":[33],"In":[34],"we":[38,48,71],"assume":[39],"only":[44],"continuous.":[45],"This":[46],"way":[47],"extend":[49],"applicability":[51],"include":[56,121],"fractional":[57,122,127,132],"calculus":[58,123,135],"and":[59,84,129],"problems":[60],"from":[61],"other":[62],"areas.":[63],"Moreover,":[64],"under":[65],"same":[67],"or":[68],"weaker":[69,73],"conditions,":[70],"obtain":[72],"sufficient":[74],"criteria,":[76],"tighter":[77],"error":[78],"bounds":[79],"distances":[82],"at":[86],"least":[87],"as":[88],"precise":[89],"information":[90],"location":[93],"solution.":[96],"Special":[97],"cases":[98],"are":[99],"provided":[100],"where":[101],"old":[103],"criteria":[105,111],"cannot":[106],"apply":[107,113],"but":[108],"new":[110],"can":[112],"locate":[115],"zeros":[116],"operators.":[118],"Some":[119],"applications":[120,141],"involving":[124],"Riemann-Liouville":[126],"integral":[128],"Caputo":[131],"derivative.":[133],"Fractional":[134],"very":[137],"important":[138],"for":[139],"its":[140],"in":[142],"many":[143],"applied":[144],"sciences.":[145]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-18T10:00:31.954636","created_date":"2025-10-10T00:00:00"}