{"id":"https://openalex.org/W2108904008","doi":"https://doi.org/10.1155/2011/726020","title":"Stability and Superstability of Generalized (<i>\u03b8</i>, <i>\u03d5</i>)\u2010Derivations in Non\u2010Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation","display_name":"Stability and Superstability of Generalized (<i>\u03b8</i>, <i>\u03d5</i>)\u2010Derivations in Non\u2010Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2108904008","doi":"https://doi.org/10.1155/2011/726020","mag":"2108904008"},"language":"en","primary_location":{"id":"doi:10.1155/2011/726020","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/726020","pdf_url":"https://downloads.hindawi.com/journals/jam/2011/726020.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2011/726020.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067866161","display_name":"M\u200e. \u200eEshaghi Gordji","orcid":"https://orcid.org/0000-0002-0077-1142"},"institutions":[{"id":"https://openalex.org/I928334797","display_name":"Semnan University","ror":"https://ror.org/029gksw03","country_code":"IR","type":"education","lineage":["https://openalex.org/I928334797"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"M. Eshaghi Gordji","raw_affiliation_strings":["Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran","Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran","institution_ids":["https://openalex.org/I928334797"]},{"raw_affiliation_string":"Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan","institution_ids":["https://openalex.org/I928334797"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078096679","display_name":"Mohammad Bagher Ghaemi","orcid":"https://orcid.org/0000-0002-6228-2395"},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"M. B. Ghaemi","raw_affiliation_strings":["Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran","Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran","institution_ids":["https://openalex.org/I67009956"]},{"raw_affiliation_string":"Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran","institution_ids":["https://openalex.org/I67009956"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089954005","display_name":"Gwang Hui Kim","orcid":"https://orcid.org/0000-0002-4279-8992"},"institutions":[{"id":"https://openalex.org/I204954614","display_name":"Kangnam University","ror":"https://ror.org/00ea13906","country_code":"KR","type":"education","lineage":["https://openalex.org/I204954614"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"G. H. Kim","raw_affiliation_strings":["Department of Mathematics, Kangnam University, Yongin, Gyeonggi 446-702, Republic of Korea","Department of Mathematics, Kangnam University, Yongin, Gyeonggi 446-702"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Kangnam University, Yongin, Gyeonggi 446-702, Republic of Korea","institution_ids":["https://openalex.org/I204954614"]},{"raw_affiliation_string":"Department of Mathematics, Kangnam University, Yongin, Gyeonggi 446-702","institution_ids":["https://openalex.org/I204954614"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083639247","display_name":"Badrkhan Alizadeh","orcid":null},"institutions":[{"id":"https://openalex.org/I4210089766","display_name":"Technical and Vocational University","ror":"https://ror.org/00854zy02","country_code":"IR","type":"education","lineage":["https://openalex.org/I4210089766"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Badrkhan Alizadeh","raw_affiliation_strings":["Technical and Vocational Faculty of Tabriz, Technical and Vocational University of Iran, P.O. Box 51745-135, Tabriz, Iran","Technical and Vocational Faculty of Tabriz, Technical and Vocational University of Iran, P.O. Box 51745-135, Tabriz"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technical and Vocational Faculty of Tabriz, Technical and Vocational University of Iran, P.O. Box 51745-135, Tabriz, Iran","institution_ids":["https://openalex.org/I4210089766"]},{"raw_affiliation_string":"Technical and Vocational Faculty of Tabriz, Technical and Vocational University of Iran, P.O. Box 51745-135, Tabriz","institution_ids":["https://openalex.org/I4210089766"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5089954005"],"corresponding_institution_ids":["https://openalex.org/I204954614"],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17649822,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2011","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12508","display_name":"Functional Equations Stability Results","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12508","display_name":"Functional Equations Stability Results","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9871000051498413,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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":0.8635322451591492},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.6831255555152893},{"id":"https://openalex.org/keywords/functional-equation","display_name":"Functional equation","score":0.6522636413574219},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.600544810295105},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.5652832984924316},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.549934983253479},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4611843228340149},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.4237965941429138},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2437630295753479},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.11662757396697998},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.04647296667098999}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8635322451591492},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.6831255555152893},{"id":"https://openalex.org/C153576954","wikidata":"https://www.wikidata.org/wiki/Q594452","display_name":"Functional equation","level":3,"score":0.6522636413574219},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.600544810295105},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.5652832984924316},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.549934983253479},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4611843228340149},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.4237965941429138},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2437630295753479},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.11662757396697998},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.04647296667098999},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2011/726020","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/726020","pdf_url":"https://downloads.hindawi.com/journals/jam/2011/726020.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1331818685","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1331818685","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:c896fec08ec34b68a7c503c325cb2fc4","is_oa":true,"landing_page_url":"https://doaj.org/article/c896fec08ec34b68a7c503c325cb2fc4","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":"Journal of Applied Mathematics, Vol 2011 (2011)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2011/726020","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/726020","pdf_url":"https://downloads.hindawi.com/journals/jam/2011/726020.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4887820330","display_name":null,"funder_award_id":"2011-0005197","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"}],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320322349","display_name":"Ministry of Education, Science and Technology","ror":"https://ror.org/01p262204"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2108904008.pdf","grobid_xml":"https://content.openalex.org/works/W2108904008.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W634677269","https://openalex.org/W1056724739","https://openalex.org/W1510886636","https://openalex.org/W1520128606","https://openalex.org/W1532178215","https://openalex.org/W1562133052","https://openalex.org/W1762593758","https://openalex.org/W1959881650","https://openalex.org/W1965756228","https://openalex.org/W1967765115","https://openalex.org/W1972938948","https://openalex.org/W1976438599","https://openalex.org/W1980109031","https://openalex.org/W1987702649","https://openalex.org/W1994123915","https://openalex.org/W2003874621","https://openalex.org/W2014910702","https://openalex.org/W2041951818","https://openalex.org/W2046465850","https://openalex.org/W2046922410","https://openalex.org/W2057457517","https://openalex.org/W2075328557","https://openalex.org/W2076283487","https://openalex.org/W2083552781","https://openalex.org/W2086212248","https://openalex.org/W2089937955","https://openalex.org/W2096101283","https://openalex.org/W2122176768","https://openalex.org/W2131819199","https://openalex.org/W2168666069","https://openalex.org/W2206265578","https://openalex.org/W2213851222","https://openalex.org/W2232029763","https://openalex.org/W2258883275","https://openalex.org/W2265471589","https://openalex.org/W2584931068","https://openalex.org/W2616480534","https://openalex.org/W2669714222","https://openalex.org/W3007602007","https://openalex.org/W4230267870","https://openalex.org/W4245388739","https://openalex.org/W7002443744","https://openalex.org/W7039862004"],"related_works":["https://openalex.org/W2846516035","https://openalex.org/W4249977926","https://openalex.org/W2585118952","https://openalex.org/W2012141574","https://openalex.org/W2354765335","https://openalex.org/W3123504591","https://openalex.org/W2369544116","https://openalex.org/W1691643469","https://openalex.org/W2985828462","https://openalex.org/W2072568712"],"abstract_inverted_index":{"Let":[0],"A":[1,14,21,23,62,70,72,95,97,129],"be":[2,10,76],"an":[3,65],"algebra,":[4],"and":[5],"let":[6],"\u03b8":[7,28,43,80,89,110,141],",":[8,29,59,81,90,126,142],"\u03d5":[9,30,48,82,91,115,143],"ring":[11],"automorphisms":[12],"of":[13,138,152],".":[15,63,130],"An":[16],"additive":[17,66],"mapping":[18,67],"H":[19,33,39,52,93,119],":":[20,69,94],"\u2192":[22,71,96],"is":[24,73],"called":[25],"a":[26,77,87,150],"(":[27,34,40,44,49,53,79,88,101,107,111,116,120,140],")\u2010derivation":[31,83,92],"if":[32,84],"x":[35,41,50,58,102,108,117,125],"y":[36,45,54,60,103,112,121,127],")":[37,42,46,51,55,104,109,113,118,122],"=":[38,105],"+":[47,114],"for":[56,123],"all":[57,124],"\u2208":[61,128],"Moreover,":[64],"F":[68,100,106],"said":[74],"to":[75],"generalized":[78,139],"there":[85],"exists":[86],"such":[98],"that":[99],"In":[131],"this":[132],"paper,":[133],"we":[134],"investigate":[135],"the":[136],"superstability":[137],")\u2010derivations":[144],"in":[145],"non\u2010Archimedean":[146],"algebras":[147],"by":[148],"using":[149],"version":[151],"fixed":[153],"point":[154],"theorem":[155],"via":[156],"Cauchy\u2019s":[157],"functional":[158],"equation.":[159]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2016-06-24T00:00:00"}
