{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:19:07Z","timestamp":1746803947868,"version":"3.40.5"},"reference-count":25,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100004085","name":"Ministry of Education, Science and Technology","doi-asserted-by":"publisher","award":["2012R1A1A4A01002971"],"award-info":[{"award-number":["2012R1A1A4A01002971"]}],"id":[{"id":"10.13039\/501100004085","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"We investigate the generalized Hyers-Ulam stability of a functional equationf<\/mml:mi>\u2211<\/mml:mo>j<\/mml:mi>=<\/mml:mo>1<\/mml:mn><\/mml:mrow>n<\/mml:mi><\/mml:mrow><\/mml:msubsup>\u200d<\/mml:mi><\/mml:mrow><\/mml:mrow>x<\/mml:mi><\/mml:mrow>j<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:mfenced>+<\/mml:mo>(<\/mml:mo>n<\/mml:mi>-<\/mml:mo>2<\/mml:mn>)<\/mml:mo>\u2211<\/mml:mo>j<\/mml:mi>=<\/mml:mo>1<\/mml:mn><\/mml:mrow>n<\/mml:mi><\/mml:mrow><\/mml:msubsup>\u200d<\/mml:mi><\/mml:mrow><\/mml:mrow>f<\/mml:mi>(<\/mml:mo>x<\/mml:mi><\/mml:mrow>j<\/mml:mi><\/mml:mrow><\/mml:msub>)<\/mml:mo>-<\/mml:mo>\u2211<\/mml:mo>1<\/mml:mn>\u2264<\/mml:mo>i<\/mml:mi><<\/mml:mo>j<\/mml:mi>\u2264<\/mml:mo>n<\/mml:mi><\/mml:mrow><\/mml:msub>f<\/mml:mi>(<\/mml:mo>x<\/mml:mi><\/mml:mrow>i<\/mml:mi><\/mml:mrow><\/mml:msub>+<\/mml:mo>x<\/mml:mi><\/mml:mrow>j<\/mml:mi><\/mml:mrow><\/mml:msub>)<\/mml:mo><\/mml:mrow><\/mml:mrow>=<\/mml:mo>0<\/mml:mn><\/mml:math>.<\/jats:p>","DOI":"10.1155\/2014\/184680","type":"journal-article","created":{"date-parts":[[2014,5,26]],"date-time":"2014-05-26T17:01:32Z","timestamp":1401123692000},"page":"1-9","source":"Crossref","is-referenced-by-count":0,"title":["On the Generalized Hyers-Ulam Stability of ann<\/mml:mi><\/mml:mrow><\/mml:math>-Dimensional Quadratic and Additive Type Functional Equation"],"prefix":"10.1155","volume":"2014","author":[{"given":"Yang-Hi","family":"Lee","sequence":"first","affiliation":[{"name":"Department of Mathematics Education, Gongju National University of Education, Gongju 314-711, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"year":"1960","key":"25"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.27.4.222"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/00210064"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.2307\/2042795"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1994.1211"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.7153\/mia-04-25"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.4134\/BKMS.2008.45.2.397"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1999.6546"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-99-05156-4"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.7153\/mia-09-16"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/326951"},{"issue":"29-32","key":"12","first-page":"1513","volume":"7","year":"2013","journal-title":"International Journal of Mathematical Analysis"},{"issue":"29-32","key":"13","first-page":"1557","volume":"7","year":"2013","journal-title":"International Journal of Mathematical Analysis"},{"issue":"49\u201352","key":"14","first-page":"2413","volume":"7","year":"2013","journal-title":"International Journal of Mathematical Analysis"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1155\/2007\/63239"},{"issue":"37\u201340","key":"19","first-page":"1935","volume":"7","year":"2013","journal-title":"International Journal of Mathematical Analysis"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1998.5916"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1186\/1029-242X-2011-70"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.5831\/HMJ.2012.34.1.19"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.7468\/jksmeb.2012.19.1.59"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.7153\/mia-06-08"},{"issue":"4","key":"6","first-page":"313","volume":"18","year":"2011","journal-title":"Journal of the Korea Society of Mathematical Education. Series B. The Pure and Applied Mathematics"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/504802"},{"key":"11","doi-asserted-by":"crossref","first-page":"201","DOI":"10.14403\/jcms.2012.25.2.201","volume":"25","year":"2012","journal-title":"Journal of the Chungcheong Mathematical Society"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.4134\/BKMS.2005.42.1.057"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/184680.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/184680.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/184680.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T09:51:59Z","timestamp":1498125119000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/184680\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":25,"alternative-id":["184680","184680"],"URL":"https:\/\/doi.org\/10.1155\/2014\/184680","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}