{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:06Z","timestamp":1740134526171,"version":"3.37.3"},"reference-count":8,"publisher":"Wiley","license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002701","name":"Ministry of Education","doi-asserted-by":"publisher","award":["2015R1D1A1A02061826"],"award-info":[{"award-number":["2015R1D1A1A02061826"]}],"id":[{"id":"10.13039\/501100002701","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2016]]},"abstract":"<jats:p>We investigate the general functional equation of the form<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>f<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>a<\/mml:mi><mml:mi>x<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>b<\/mml:mi><mml:mi>y<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>c<\/mml:mi><mml:mi>z<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>-<\/mml:mo><mml:mi>a<\/mml:mi><mml:mi>b<\/mml:mi><mml:mi>f<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>y<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>-<\/mml:mo><mml:mi>b<\/mml:mi><mml:mi>c<\/mml:mi><mml:mi>f<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>y<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>z<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>\u2212<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>a<\/mml:mi><mml:mi>c<\/mml:mi><mml:mi>f<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>z<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>-<\/mml:mo><mml:mi>a<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>a<\/mml:mi><mml:mo>+<\/mml:mo><mml:mn mathvariant=\"normal\">1<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>\/<\/mml:mo><mml:mn mathvariant=\"normal\">2<\/mml:mn><mml:mo>-<\/mml:mo><mml:mi>b<\/mml:mi><mml:mo>-<\/mml:mo><mml:mi>c<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mi>f<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>-<\/mml:mo><mml:mi>b<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>b<\/mml:mi><mml:mo>+<\/mml:mo><mml:mn mathvariant=\"normal\">1<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>\/<\/mml:mo><mml:mn mathvariant=\"normal\">2<\/mml:mn><mml:mo>-<\/mml:mo><mml:mi>a<\/mml:mi><mml:mo>-<\/mml:mo><mml:mi>c<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mi>f<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>y<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>-<\/mml:mo><mml:mi>c<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>c<\/mml:mi><mml:mo>+<\/mml:mo><mml:mn mathvariant=\"normal\">1<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>\/<\/mml:mo><mml:mn mathvariant=\"normal\">2<\/mml:mn><mml:mo>-<\/mml:mo><mml:mi>a<\/mml:mi><mml:mo>-<\/mml:mo><mml:mi>b<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mi>f<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>z<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>-<\/mml:mo><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>a<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>a<\/mml:mi><mml:mo>-<\/mml:mo><mml:mn mathvariant=\"normal\">1<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>\/<\/mml:mo><mml:mn mathvariant=\"normal\">2<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mi>f<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mo>-<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>\u2212<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>b<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>b<\/mml:mi><mml:mo>-<\/mml:mo><mml:mn mathvariant=\"normal\">1<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>\/<\/mml:mo><mml:mn mathvariant=\"normal\">2<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mi>f<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mo>-<\/mml:mo><mml:mi>y<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>-<\/mml:mo><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>c<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>c<\/mml:mi><mml:mo>-<\/mml:mo><mml:mn mathvariant=\"normal\">1<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>\/<\/mml:mo><mml:mn mathvariant=\"normal\">2<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mi>f<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mo>-<\/mml:mo><mml:mi>z<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>=<\/mml:mo><mml:mn mathvariant=\"normal\">0<\/mml:mn><\/mml:math>, whose solutions are quadratic-additive mappings in connection with stability problems.<\/jats:p>","DOI":"10.1155\/2016\/1793065","type":"journal-article","created":{"date-parts":[[2016,5,23]],"date-time":"2016-05-23T13:10:43Z","timestamp":1464009043000},"page":"1-10","source":"Crossref","is-referenced-by-count":0,"title":["General Quadratic-Additive Type Functional Equation and Its Stability"],"prefix":"10.1155","volume":"2016","author":[{"given":"Yang-Hi","family":"Lee","sequence":"first","affiliation":[{"name":"Department of Mathematics Education, Gongju National University of Education, Gongju 32553, Republic of 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