{"id":"https://openalex.org/W4406332101","doi":"https://doi.org/10.3390/sym17010112","title":"On Ulam Stability of Functional Equations in Non-Archimedean Spaces","display_name":"On Ulam Stability of Functional Equations in Non-Archimedean Spaces","publication_year":2025,"publication_date":"2025-01-13","ids":{"openalex":"https://openalex.org/W4406332101","doi":"https://doi.org/10.3390/sym17010112"},"language":"en","primary_location":{"id":"doi:10.3390/sym17010112","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010112","pdf_url":"https://www.mdpi.com/2073-8994/17/1/112/pdf?version=1736758968","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/2073-8994/17/1/112/pdf?version=1736758968","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075702494","display_name":"Krzysztof Ciepli\u0144ski","orcid":"https://orcid.org/0000-0003-3050-7841"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]},{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Krzysztof Ciepli\u0144ski","raw_affiliation_strings":["Faculty of Applied Mathematics, AGH University of Krakow, Mickiewicza 30, 30-059 Krak\u00f3w, Poland"],"affiliations":[{"raw_affiliation_string":"Faculty of Applied Mathematics, AGH University of Krakow, Mickiewicza 30, 30-059 Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I686019","https://openalex.org/I126596746"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5075702494"],"corresponding_institution_ids":["https://openalex.org/I126596746","https://openalex.org/I686019"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":7.7212,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.95039164,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"17","issue":"1","first_page":"112","last_page":"112"},"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":0.9832000136375427,"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":0.9427000284194946,"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/functional-equation","display_name":"Functional equation","score":0.7770342826843262},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7646420001983643},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5911445617675781},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.4665749967098236},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4254502058029175},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39183878898620605},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35156846046447754},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.3203730583190918},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09039425849914551}],"concepts":[{"id":"https://openalex.org/C153576954","wikidata":"https://www.wikidata.org/wiki/Q594452","display_name":"Functional equation","level":3,"score":0.7770342826843262},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7646420001983643},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5911445617675781},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.4665749967098236},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4254502058029175},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39183878898620605},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35156846046447754},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3203730583190918},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09039425849914551},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym17010112","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010112","pdf_url":"https://www.mdpi.com/2073-8994/17/1/112/pdf?version=1736758968","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:70595dae0d08484e9476e02f9c003341","is_oa":true,"landing_page_url":"https://doaj.org/article/70595dae0d08484e9476e02f9c003341","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 17, Iss 1, p 112 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym17010112","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010112","pdf_url":"https://www.mdpi.com/2073-8994/17/1/112/pdf?version=1736758968","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406332101.pdf","grobid_xml":"https://content.openalex.org/works/W4406332101.grobid-xml"},"referenced_works_count":87,"referenced_works":["https://openalex.org/W32833610","https://openalex.org/W308301644","https://openalex.org/W392395549","https://openalex.org/W576288110","https://openalex.org/W593642458","https://openalex.org/W634677269","https://openalex.org/W1495535461","https://openalex.org/W1501503542","https://openalex.org/W1532178215","https://openalex.org/W1562133052","https://openalex.org/W1595749660","https://openalex.org/W1964426670","https://openalex.org/W1968796899","https://openalex.org/W1971108773","https://openalex.org/W1971465402","https://openalex.org/W1976242878","https://openalex.org/W1987702649","https://openalex.org/W1993677455","https://openalex.org/W1998856232","https://openalex.org/W2003874621","https://openalex.org/W2005186233","https://openalex.org/W2009064211","https://openalex.org/W2012981171","https://openalex.org/W2035892959","https://openalex.org/W2036323079","https://openalex.org/W2046465850","https://openalex.org/W2052145511","https://openalex.org/W2078124339","https://openalex.org/W2082153070","https://openalex.org/W2083971740","https://openalex.org/W2088145369","https://openalex.org/W2090173195","https://openalex.org/W2098066898","https://openalex.org/W2113977577","https://openalex.org/W2130350211","https://openalex.org/W2130731719","https://openalex.org/W2133279605","https://openalex.org/W2135084707","https://openalex.org/W2135541428","https://openalex.org/W2154380825","https://openalex.org/W2159460112","https://openalex.org/W2166890456","https://openalex.org/W2206265578","https://openalex.org/W2213851222","https://openalex.org/W2314755574","https://openalex.org/W2333976070","https://openalex.org/W2345923978","https://openalex.org/W2614662766","https://openalex.org/W2614736323","https://openalex.org/W2769561680","https://openalex.org/W2792761023","https://openalex.org/W2804306326","https://openalex.org/W2806926977","https://openalex.org/W2959650376","https://openalex.org/W2962944780","https://openalex.org/W2963562046","https://openalex.org/W2993297753","https://openalex.org/W3029540217","https://openalex.org/W3039943884","https://openalex.org/W3102058873","https://openalex.org/W3103345357","https://openalex.org/W3163248253","https://openalex.org/W3170682948","https://openalex.org/W3192176929","https://openalex.org/W3213077971","https://openalex.org/W4205809535","https://openalex.org/W4205978069","https://openalex.org/W4210770667","https://openalex.org/W4210945509","https://openalex.org/W4230656811","https://openalex.org/W4232780126","https://openalex.org/W4251520976","https://openalex.org/W4283809993","https://openalex.org/W4315642798","https://openalex.org/W4391746243","https://openalex.org/W4392306772","https://openalex.org/W4394847781","https://openalex.org/W6629588261","https://openalex.org/W6676351199","https://openalex.org/W6676714619","https://openalex.org/W6688100596","https://openalex.org/W6688713792","https://openalex.org/W6771483203","https://openalex.org/W6778247803","https://openalex.org/W6785630245","https://openalex.org/W6807891103","https://openalex.org/W6888849585"],"related_works":["https://openalex.org/W4313430702","https://openalex.org/W2080368266","https://openalex.org/W2035892959","https://openalex.org/W2329589267","https://openalex.org/W2367928013","https://openalex.org/W2371924662","https://openalex.org/W2024029025","https://openalex.org/W2169334821","https://openalex.org/W2075507855","https://openalex.org/W2243533358"],"abstract_inverted_index":{"We":[0,16],"present":[1],"a":[2,43,46,50],"survey":[3],"of":[4,9],"outcomes":[5],"on":[6,19,45],"Ulam":[7],"stability":[8],"functional":[10,20,62],"equations":[11,21],"in":[12,22,49],"non-Archimedean":[13],"normed":[14],"spaces.":[15,87],"focus":[17],"mainly":[18],"several":[23],"variables":[24],"(including":[25],"the":[26,29,33,58,71,74,78],"Cauchy":[27],"equation,":[28,32,35],"Jordan\u2013von":[30],"Neumann":[31],"Jensen":[34],"and":[36,77,85],"their":[37],"generalizations),":[38],"but":[39],"we":[40],"also":[41],"report":[42],"result":[44],"general":[47],"equation":[48],"single":[51],"variable,":[52],"which":[53],"can":[54,69],"be":[55],"applied":[56],"to":[57],"very":[59],"important":[60],"linear":[61],"equation.":[63],"Let":[64],"us":[65],"note":[66],"that":[67],"one":[68],"observe":[70],"symmetry":[72],"between":[73],"presented":[75],"results":[76],"analogous":[79],"ones":[80],"obtained":[81],"for":[82],"both":[83],"classical":[84],"two-normed":[86]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
