{"id":"https://openalex.org/W4286500904","doi":"https://doi.org/10.3390/sym14071484","title":"Extended Convergence of Three Step Iterative Methods for Solving Equations in Banach Space with Applications","display_name":"Extended Convergence of Three Step Iterative Methods for Solving Equations in Banach Space with Applications","publication_year":2022,"publication_date":"2022-07-20","ids":{"openalex":"https://openalex.org/W4286500904","doi":"https://doi.org/10.3390/sym14071484"},"language":"en","primary_location":{"id":"doi:10.3390/sym14071484","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14071484","pdf_url":"https://www.mdpi.com/2073-8994/14/7/1484/pdf?version=1658306103","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/7/1484/pdf?version=1658306103","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068409818","display_name":"Samundra Regmi","orcid":"https://orcid.org/0000-0003-0035-1022"},"institutions":[{"id":"https://openalex.org/I44461941","display_name":"University of Houston","ror":"https://ror.org/048sx0r50","country_code":"US","type":"education","lineage":["https://openalex.org/I44461941"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Samundra Regmi","raw_affiliation_strings":["Department of Mathematics, University of Houston, Houston, TX 77204, USA"],"raw_orcid":"https://orcid.org/0000-0003-0035-1022","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Houston, Houston, TX 77204, USA","institution_ids":["https://openalex.org/I44461941"]}]},{"author_position":"middle","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 Mathematical Sciences, Cameron University, Lawton, OK 73505, USA"],"raw_orcid":"https://orcid.org/0000-0002-9189-9298","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA","institution_ids":["https://openalex.org/I113618177"]}]},{"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, Mangaluru 575 025, India"],"raw_orcid":"https://orcid.org/0000-0002-3530-5539","affiliations":[{"raw_affiliation_string":"Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangaluru 575 025, India","institution_ids":["https://openalex.org/I11880225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059808785","display_name":"Christopher I. Argyros","orcid":"https://orcid.org/0000-0002-7647-3571"},"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":"Christopher I. Argyros","raw_affiliation_strings":["Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA","institution_ids":["https://openalex.org/I113618177"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5068409818"],"corresponding_institution_ids":["https://openalex.org/I44461941"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.9606,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.70168993,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"14","issue":"7","first_page":"1484","last_page":"1484"},"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":0.9950000047683716,"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":0.9919999837875366,"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/banach-space","display_name":"Banach space","score":0.7202962040901184},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.656501054763794},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5666804313659668},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.5492833852767944},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5339324474334717},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5326012969017029},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.5237138867378235},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5171108245849609},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5045546293258667},{"id":"https://openalex.org/keywords/contrast","display_name":"Contrast (vision)","score":0.4738467335700989},{"id":"https://openalex.org/keywords/simultaneous-equations","display_name":"Simultaneous equations","score":0.43165791034698486},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3453395962715149},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3031885325908661},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3003736734390259},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.08429330587387085},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07148906588554382},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06498551368713379}],"concepts":[{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.7202962040901184},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.656501054763794},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5666804313659668},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.5492833852767944},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5339324474334717},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5326012969017029},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.5237138867378235},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5171108245849609},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5045546293258667},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.4738467335700989},{"id":"https://openalex.org/C170036204","wikidata":"https://www.wikidata.org/wiki/Q735660","display_name":"Simultaneous equations","level":3,"score":0.43165791034698486},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3453395962715149},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3031885325908661},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3003736734390259},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.08429330587387085},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07148906588554382},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06498551368713379},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"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/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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14071484","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14071484","pdf_url":"https://www.mdpi.com/2073-8994/14/7/1484/pdf?version=1658306103","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:94c4f45bc94a4b44861de772433cbb2e","is_oa":true,"landing_page_url":"https://doaj.org/article/94c4f45bc94a4b44861de772433cbb2e","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":"Symmetry, Vol 14, Iss 7, p 1484 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/7/1484/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14071484","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":"Symmetry; Volume 14; Issue 7; Pages: 1484","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14071484","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14071484","pdf_url":"https://www.mdpi.com/2073-8994/14/7/1484/pdf?version=1658306103","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4286500904.pdf"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1968908233","https://openalex.org/W1982246852","https://openalex.org/W2001804618","https://openalex.org/W2006219706","https://openalex.org/W2022703159","https://openalex.org/W2038843446","https://openalex.org/W2054204520","https://openalex.org/W2073765564","https://openalex.org/W2615379274","https://openalex.org/W2782519404","https://openalex.org/W3168352518","https://openalex.org/W3195146610","https://openalex.org/W4210533869","https://openalex.org/W6645806630","https://openalex.org/W6738072560"],"related_works":["https://openalex.org/W2378562963","https://openalex.org/W2350788688","https://openalex.org/W2353579944","https://openalex.org/W2089967807","https://openalex.org/W2078306205","https://openalex.org/W2033997865","https://openalex.org/W2031390949","https://openalex.org/W4378376763","https://openalex.org/W2924965583","https://openalex.org/W1964706674"],"abstract_inverted_index":{"Symmetries":[0],"are":[1,33],"vital":[2],"in":[3,26,31,71,76],"the":[4,14,40,86,91],"study":[5,52],"of":[6,42,85],"physical":[7],"phenomena":[8,20],"such":[9],"as":[10],"quantum":[11],"physics":[12],"and":[13],"micro-world,":[15],"among":[16],"others.":[17],"Then,":[18],"these":[19,72],"reduce":[21],"to":[22,46,51,56,78,89],"solving":[23],"nonlinear":[24],"equations":[25,30,58],"abstract":[27],"spaces.":[28,62],"These":[29],"turn":[32],"mostly":[34],"solved":[35],"iteratively.":[36],"That":[37],"is":[38,65,75],"why":[39],"objective":[41],"this":[43,97],"paper":[44],"was":[45],"obtain":[47],"a":[48],"uniform":[49],"way":[50],"three-step":[53],"iterative":[54],"methods":[55],"solve":[57],"defined":[59],"on":[60,83],"Banach":[61],"The":[63,93],"convergence":[64],"established":[66],"by":[67],"using":[68],"information":[69],"appearing":[70],"methods.":[73],"This":[74],"contrast":[77],"earlier":[79],"works":[80],"which":[81],"relied":[82],"derivatives":[84],"higher":[87],"order":[88],"establish":[90],"convergence.":[92],"numerical":[94],"example":[95],"completes":[96],"paper.":[98]},"counts_by_year":[{"year":2024,"cited_by_count":3}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}