Two step Steffensen-type methods with or without memory for nondifferentiable equations

A wide range of applications emerging from diverse disciplines are formulated as an equation or system of equations in abstract spaces such as Euclidean multidimensional, Hilbert or Banach to mention a few, a plethora of which are nondifferentiable. Different methodologies are developed worldwide to...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Journal of numerical analysis and approximation theory
Hlavní autori: Argyros, Ioannis K., Deep, Gagan
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Publishing House of the Romanian Academy 03.10.2025
Predmet:
Banach space
Convergence
divided difference
Steffensen-type method
ISSN:2457-6794, 2501-059X
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Abstract A wide range of applications emerging from diverse disciplines are formulated as an equation or system of equations in abstract spaces such as Euclidean multidimensional, Hilbert or Banach to mention a few, a plethora of which are nondifferentiable. Different methodologies are developed worldwide to handle the solutions of such equations. Such methodologies can also be applied to solve the differentiable equations. In the current study, two step Steffensen-Type methods with and without memory free from derivatives are considered for the nondifferentiable equations and the local as well as semilocal convergence analysis is proved under more generalized conditions. Numerical applications are provided which demonstrate the theoretical results. Better results in terms of radii of convergence balls and number of iterations are obtained using the proposed approach as compared to the existing ones.
AbstractList A wide range of applications emerging from diverse disciplines are formulated as an equation or system of equations in abstract spaces such as Euclidean multidimensional, Hilbert or Banach to mention a few, a plethora of which are nondifferentiable. Different methodologies are developed worldwide to handle the solutions of such equations. Such methodologies can also be applied to solve the differentiable equations. In the current study, two step Steffensen-Type methods with and without memory free from derivatives are considered for the nondifferentiable equations and the local as well as semilocal convergence analysis is proved under more generalized conditions. Numerical applications are provided which demonstrate the theoretical results. Better results in terms of radii of convergence balls and number of iterations are obtained using the proposed approach as compared to the existing ones.
Author Deep, Gagan
Argyros, Ioannis K.
Author_xml – sequence: 1
  givenname: Ioannis K.
  surname: Argyros
  fullname: Argyros, Ioannis K.
– sequence: 2
  givenname: Gagan
  orcidid: 0000-0002-2668-3079
  surname: Deep
  fullname: Deep, Gagan
BookMark eNo9kE1LAzEQhoMoqLVXz_sHVvO5SY5S_CgUPFjRW0h2J3ZLu6lJSum_N23Vy8zwwDy8vNfofAgDIHRL8B1jWrP75WBtFpzWhAt5hq6owKTGQn-el7ugupGaX6JxSkuMMZGUcUWu0Md8F6qUYVO9ZfAehgRDnfcbqNaQF6FL1a7PiyrE4w7bXPg6xH3lCyoZur48RRhyb90KKvje2tyHId2gC29XCca_e4Tenx7nk5d69vo8nTzM6vaQs3aqoa5Vnejajkouue8aBY5hSyQjrQPMmBSKMaWZAKK8JoRYqmkLruXg2QhNT94u2KXZxH5t494E25sjCPHL2Jj7dgXGukZY5sqUjFsltOSCaqFsxygmuimuu5OrjSGlCP7fR7A5tmz-WjaH9OwHPZdzGg
Cites_doi 10.3390/foundations3020014
10.1016/j.jco.2019.02.003
10.1007/s00009-022-02030-5
10.1007/s11075-015-0003-9
10.3390/foundations3010009
10.1007/s10910-019-01097-y
10.1016/j.aml.2020.106277
10.1007/s41478-022-00505-y
10.1007/s40819-020-0784-y
10.1016/j.amc.2007.01.062
10.1016/j.cam.2018.10.048
10.1007/s11075-012-9585-7
10.1007/s41478-019-00216-x
10.3390/foundations3010003
10.1080/00207160.2012.737461
10.1016/j.cam.2010.09.019
ContentType Journal Article
DBID AAYXX
CITATION
DOA
DOI 10.33993/jnaat542-1457
DatabaseName CrossRef
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
DatabaseTitleList
CrossRef
Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
DeliveryMethod fulltext_linktorsrc
Discipline Applied Sciences
EISSN 2501-059X
ExternalDocumentID oai_doaj_org_article_ab65a3bb65734a8597452958ad320196
10_33993_jnaat542_1457
GroupedDBID AAYXX
ALMA_UNASSIGNED_HOLDINGS
CITATION
GROUPED_DOAJ
ID FETCH-LOGICAL-c1457-b862bc8d5dcd27474fd68eb30a1731cbe033758338935e18f9111a292cebc4ef3
IEDL.DBID DOA
ISSN 2457-6794
IngestDate Mon Oct 13 19:20:23 EDT 2025
Thu Oct 09 00:34:17 EDT 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Language English
License https://creativecommons.org/licenses/by/4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c1457-b862bc8d5dcd27474fd68eb30a1731cbe033758338935e18f9111a292cebc4ef3
ORCID 0000-0002-2668-3079
OpenAccessLink https://doaj.org/article/ab65a3bb65734a8597452958ad320196
ParticipantIDs doaj_primary_oai_doaj_org_article_ab65a3bb65734a8597452958ad320196
crossref_primary_10_33993_jnaat542_1457
PublicationCentury 2000
PublicationDate 2025-10-03
PublicationDateYYYYMMDD 2025-10-03
PublicationDate_xml – month: 10
  year: 2025
  text: 2025-10-03
  day: 03
PublicationDecade 2020
PublicationTitle Journal of numerical analysis and approximation theory
PublicationYear 2025
Publisher Publishing House of the Romanian Academy
Publisher_xml – name: Publishing House of the Romanian Academy
References 39241
39252
39263
39251
39262
39243
39254
39242
39253
39264
39245
39256
39244
39255
39247
39258
39246
39257
39250
39261
39260
39249
39248
39259
References_xml – ident: 39256
  doi: 10.3390/foundations3020014
– ident: 39261
  doi: 10.1016/j.jco.2019.02.003
– ident: 39264
  doi: 10.1007/s00009-022-02030-5
– ident: 39263
– ident: 39255
  doi: 10.1007/s11075-015-0003-9
– ident: 39241
  doi: 10.3390/foundations3010009
– ident: 39252
  doi: 10.1007/s10910-019-01097-y
– ident: 39257
– ident: 39259
– ident: 39254
– ident: 39249
– ident: 39246
  doi: 10.1016/j.aml.2020.106277
– ident: 39251
– ident: 39260
  doi: 10.1007/s41478-022-00505-y
– ident: 39244
  doi: 10.1007/s40819-020-0784-y
– ident: 39247
  doi: 10.1016/j.amc.2007.01.062
– ident: 39253
  doi: 10.1016/j.cam.2018.10.048
– ident: 39258
  doi: 10.1007/s11075-012-9585-7
– ident: 39262
  doi: 10.1007/s41478-019-00216-x
– ident: 39248
  doi: 10.3390/foundations3010003
– ident: 39242
– ident: 39245
– ident: 39243
  doi: 10.1080/00207160.2012.737461
– ident: 39250
  doi: 10.1016/j.cam.2010.09.019
SSID ssj0001723481
Score 2.3052065
Snippet A wide range of applications emerging from diverse disciplines are formulated as an equation or system of equations in abstract spaces such as Euclidean...
SourceID doaj
crossref
SourceType Open Website
Index Database
SubjectTerms Banach space
Convergence
divided difference
Steffensen-type method
Title Two step Steffensen-type methods with or without memory for nondifferentiable equations
URI https://doaj.org/article/ab65a3bb65734a8597452958ad320196
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAON
  databaseName: DOAJ Directory of Open Access Journals
  customDbUrl:
  eissn: 2501-059X
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0001723481
  issn: 2457-6794
  databaseCode: DOA
  dateStart: 20220101
  isFulltext: true
  titleUrlDefault: https://www.doaj.org/
  providerName: Directory of Open Access Journals
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LS8QwEA6yePDiW1xf5CB4Cts2SZMeVVw8LYIr7q0kaQKK7q5tV_HfO9N2pTcvXloIoQ0zSeaRzPcRculhi_NBGiZjnzIhjGKGY4FPFhdgcdFG2YZsQk0mejbLHnpUX3gnrIUHbgU3MjaVhlt4Ki6MRv8Xz6a0KXiC2C64-0Yq6wVTTXZFJVhhisxyQiqWwqxrERs5GuTR69yYWoqExQLtUs8i9YD7Gwsz3iXbnWtIr9sh7ZENP98nO52bSLtFWB2Q5-nXgoJylvSxxusYmB1mmEqlLR10RTG5Shdl816samh_X5TfFPxTCtH-mhMF1rZ989R_tGjf1SF5Gt9Nb-9Zx4_AHI6bWYhGrNOFLFyBwaUIRaohOI5MrHjsrI84V1hVBT6J9LEOuLGZJEuct074wI_IAP7qjwnVyjrFg3LWgtyCsVkcIhVsIrXOggxDcrWWUb5sYTByCB8aaeZraeY4qiG5QRH-9kL46qYBlJp3Ss3_UurJf3zklGwlSNaLp_38jAzqcuXPyab7rF-q8qKZLz_F58Lv
linkProvider Directory of Open Access Journals
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Two+step+Steffensen-type+methods+with+or+without+memory+for+nondifferentiable+equations&rft.jtitle=Journal+of+numerical+analysis+and+approximation+theory&rft.au=Ioannis+K.+Argyros&rft.au=Gagan+Deep&rft.date=2025-10-03&rft.pub=Publishing+House+of+the+Romanian+Academy&rft.issn=2457-6794&rft.eissn=2501-059X&rft_id=info:doi/10.33993%2Fjnaat542-1457&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_ab65a3bb65734a8597452958ad320196
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2457-6794&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2457-6794&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2457-6794&client=summon