{"id":"https://openalex.org/W4400774076","doi":"https://doi.org/10.3390/axioms13070480","title":"Stability Results for Some Classes of Cubic Functional Equations","display_name":"Stability Results for Some Classes of Cubic Functional Equations","publication_year":2024,"publication_date":"2024-07-18","ids":{"openalex":"https://openalex.org/W4400774076","doi":"https://doi.org/10.3390/axioms13070480"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13070480","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13070480","pdf_url":"https://www.mdpi.com/2075-1680/13/7/480/pdf?version=1721351921","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/2075-1680/13/7/480/pdf?version=1721351921","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083999319","display_name":"El\u2010sayed El\u2010hady","orcid":"https://orcid.org/0000-0002-4955-0842"},"institutions":[{"id":"https://openalex.org/I199702508","display_name":"Jouf University","ror":"https://ror.org/02zsyt821","country_code":"SA","type":"education","lineage":["https://openalex.org/I199702508"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"El-sayed El-hady","raw_affiliation_strings":["Mathematics Department, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-4955-0842","affiliations":[{"raw_affiliation_string":"Mathematics Department, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia","institution_ids":["https://openalex.org/I199702508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001678349","display_name":"Yamin Sayyari","orcid":"https://orcid.org/0000-0001-8019-3655"},"institutions":[{"id":"https://openalex.org/I170905427","display_name":"Sirjan University of Technology","ror":"https://ror.org/023tdry64","country_code":"IR","type":"education","lineage":["https://openalex.org/I170905427"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Yamin Sayyari","raw_affiliation_strings":["Department of Mathematics, Sirjan University of Technology, Sirjan 7813733385, Iran"],"raw_orcid":"https://orcid.org/0000-0001-8019-3655","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sirjan University of Technology, Sirjan 7813733385, Iran","institution_ids":["https://openalex.org/I170905427"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088418567","display_name":"Mehdi Dehghanian","orcid":"https://orcid.org/0000-0002-5348-1333"},"institutions":[{"id":"https://openalex.org/I170905427","display_name":"Sirjan University of Technology","ror":"https://ror.org/023tdry64","country_code":"IR","type":"education","lineage":["https://openalex.org/I170905427"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mehdi Dehghanian","raw_affiliation_strings":["Department of Mathematics, Sirjan University of Technology, Sirjan 7813733385, Iran"],"raw_orcid":"https://orcid.org/0000-0002-5348-1333","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sirjan University of Technology, Sirjan 7813733385, Iran","institution_ids":["https://openalex.org/I170905427"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067561732","display_name":"Ymnah Alruwaily","orcid":"https://orcid.org/0000-0001-6562-9705"},"institutions":[{"id":"https://openalex.org/I199702508","display_name":"Jouf University","ror":"https://ror.org/02zsyt821","country_code":"SA","type":"education","lineage":["https://openalex.org/I199702508"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Ymnah Alruwaily","raw_affiliation_strings":["Mathematics Department, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-6562-9705","affiliations":[{"raw_affiliation_string":"Mathematics Department, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia","institution_ids":["https://openalex.org/I199702508"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5067561732","https://openalex.org/A5083999319"],"corresponding_institution_ids":["https://openalex.org/I199702508"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.8653,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.69405467,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"13","issue":"7","first_page":"480","last_page":"480"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12508","display_name":"Functional Equations Stability Results","score":1.0,"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":1.0,"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":0.980400025844574,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9664999842643738,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5352441072463989},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4299928545951843},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24338608980178833},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.05007407069206238}],"concepts":[{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5352441072463989},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4299928545951843},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24338608980178833},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.05007407069206238}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13070480","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13070480","pdf_url":"https://www.mdpi.com/2075-1680/13/7/480/pdf?version=1721351921","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:5f71a9abbc384ca98bb5c34f90dc4864","is_oa":true,"landing_page_url":"https://doaj.org/article/5f71a9abbc384ca98bb5c34f90dc4864","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 13, Iss 7, p 480 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13070480","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13070480","pdf_url":"https://www.mdpi.com/2075-1680/13/7/480/pdf?version=1721351921","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/W4400774076.pdf","grobid_xml":"https://content.openalex.org/works/W4400774076.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W593642458","https://openalex.org/W823443743","https://openalex.org/W1532178215","https://openalex.org/W1552892605","https://openalex.org/W1987702649","https://openalex.org/W2003874621","https://openalex.org/W2006316635","https://openalex.org/W2006384207","https://openalex.org/W2009174170","https://openalex.org/W2035907710","https://openalex.org/W2042047534","https://openalex.org/W2057230989","https://openalex.org/W2057485405","https://openalex.org/W2070134232","https://openalex.org/W2153013525","https://openalex.org/W2323711820","https://openalex.org/W2350052830","https://openalex.org/W2513173310","https://openalex.org/W2529556795","https://openalex.org/W2911340892","https://openalex.org/W3081649597","https://openalex.org/W3134155059","https://openalex.org/W3134922546","https://openalex.org/W3213077971","https://openalex.org/W4320487829","https://openalex.org/W4321373765","https://openalex.org/W4387164404","https://openalex.org/W6623096307","https://openalex.org/W6701048181","https://openalex.org/W6996618231"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"Applications":[0],"involving":[1],"functional":[2,51],"equations":[3,52],"(FUEQs)":[4],"are":[5,8],"commonplace.":[6],"They":[7],"essential":[9],"to":[10],"various":[11],"applications,":[12],"such":[13],"as":[14],"fog":[15],"computing.":[16],"Ulam\u2019s":[17],"notion":[18],"of":[19,29,46],"stability":[20,45],"is":[21],"highly":[22],"helpful":[23],"since":[24],"it":[25],"provides":[26],"a":[27],"range":[28],"estimates":[30],"between":[31],"exact":[32],"and":[33],"approximate":[34],"solutions.":[35],"Using":[36],"Brzd\u0229k\u2019s":[37],"fixed":[38],"point":[39],"technique":[40],"(FPT),":[41],"we":[42],"establish":[43],"the":[44,47],"following":[48],"cubic":[49],"type":[50],"(CFUEQs):":[53],"F\u03be13+\u03be233+F\u03be13\u2212\u03be233=2F(\u03be1)+2F(\u03be2),2F\u03be13+\u03be2323=F(\u03be1)+F(\u03be2)":[54],"for":[55],"all":[56],"\u03be1,\u03be2\u2208R.":[57]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-10-10T00:00:00"}
