{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T21:10:01Z","timestamp":1723065001842},"reference-count":0,"publisher":"Wiley","issue":"22","license":[{"start":{"date-parts":[[2000,1,1]],"date-time":"2000-01-01T00:00:00Z","timestamp":946684800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:p>Let <jats:italic>h<\/jats:italic> be an entire function and <jats:italic>T<\/jats:italic><jats:sub><jats:italic>h<\/jats:italic><\/jats:sub> a differential operator defined by <jats:italic>T<\/jats:italic><jats:sub><jats:italic>h<\/jats:italic><\/jats:sub><jats:italic>f<\/jats:italic> = <jats:italic>f<\/jats:italic><jats:sup>\u2032<\/jats:sup> + <jats:italic>h<\/jats:italic><jats:italic>f<\/jats:italic>. We show that <jats:italic>T<\/jats:italic><jats:sub><jats:italic>h<\/jats:italic><\/jats:sub> has the Hyers\u2010Ulam stability if and only if <jats:italic>h<\/jats:italic> is a nonzero constant. We also consider Ger\u2010type stability problem for |1 \u2212 <jats:italic>f<\/jats:italic><jats:sup>\u2032<\/jats:sup>\/<jats:italic>h<\/jats:italic><jats:italic>f<\/jats:italic>| \u2264 <jats:italic>\u03f5<\/jats:italic>.<\/jats:p>","DOI":"10.1155\/s0161171204304333","type":"journal-article","created":{"date-parts":[[2004,5,24]],"date-time":"2004-05-24T18:52:40Z","timestamp":1085424760000},"page":"1151-1158","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Ger\u2010type and Hyers\u2010Ulam stabilities for the first\u2010order linear differential operators of entire functions"],"prefix":"10.1155","volume":"2004","author":[{"given":"Takeshi","family":"Miura","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Go","family":"Hirasawa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sin-Ei","family":"Takahasi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2004,5,24]]},"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2004\/756349.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/S0161171204304333","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T20:38:38Z","timestamp":1723063118000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/S0161171204304333"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":0,"journal-issue":{"issue":"22","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1155\/S0161171204304333"],"URL":"https:\/\/doi.org\/10.1155\/s0161171204304333","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2004,1]]},"assertion":[{"value":"2003-04-22","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2004-05-24","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}