{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:36:49Z","timestamp":1753886209944,"version":"3.41.2"},"reference-count":23,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,3,15]],"date-time":"2012-03-15T00:00:00Z","timestamp":1331769600000},"content-version":"vor","delay-in-days":74,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100002467","name":"Dankook University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002467","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>Let <jats:italic>G<\/jats:italic> be an Abelian group, let <jats:italic>\u2102<\/jats:italic> be the field of complex numbers, and let <jats:italic>f<\/jats:italic>, <jats:italic>g<\/jats:italic> : <jats:italic>G<\/jats:italic> \u2192 <jats:italic>\u2102<\/jats:italic>. We consider the generalized Hyers\u2010Ulam stability for a class of trigonometric functional inequalities, |<jats:italic>f<\/jats:italic>(<jats:italic>x<\/jats:italic> \u2212 <jats:italic>y<\/jats:italic>) \u2212 <jats:italic>f<\/jats:italic>(<jats:italic>x<\/jats:italic>)<jats:italic>g<\/jats:italic>(<jats:italic>y<\/jats:italic>) + <jats:italic>g<\/jats:italic>(<jats:italic>x<\/jats:italic>)<jats:italic>f<\/jats:italic>(<jats:italic>y<\/jats:italic>)| \u2264 <jats:italic>\u03c8<\/jats:italic>(<jats:italic>y<\/jats:italic>),\u2009\u2009|<jats:italic>g<\/jats:italic>(<jats:italic>x<\/jats:italic> \u2212 <jats:italic>y<\/jats:italic>) \u2212 <jats:italic>g<\/jats:italic>(<jats:italic>x<\/jats:italic>)<jats:italic>g<\/jats:italic>(<jats:italic>y<\/jats:italic>) \u2212 <jats:italic>f<\/jats:italic>(<jats:italic>x<\/jats:italic>)<jats:italic>f<\/jats:italic>(<jats:italic>y<\/jats:italic>)| \u2264 <jats:italic>\u03c8<\/jats:italic>(<jats:italic>y<\/jats:italic>), where <jats:italic>\u03c8<\/jats:italic> : <jats:italic>G<\/jats:italic> \u2192 <jats:italic>\u211d<\/jats:italic> is an arbitrary nonnegative function.<\/jats:p>","DOI":"10.1155\/2012\/610714","type":"journal-article","created":{"date-parts":[[2012,3,15]],"date-time":"2012-03-15T21:55:06Z","timestamp":1331848506000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On a Generalized Hyers\u2010Ulam Stability of Trigonometric Functional Equations"],"prefix":"10.1155","volume":"2012","author":[{"given":"Jaeyoung","family":"Chung","sequence":"first","affiliation":[]},{"given":"Jeongwook","family":"Chang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,3,15]]},"reference":[{"volume-title":"A Collection of Mathematical Problems","year":"1960","author":"Ulam S. 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