{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T22:31:00Z","timestamp":1770330660307,"version":"3.49.0"},"reference-count":17,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,9,15]],"date-time":"2011-09-15T00:00:00Z","timestamp":1316044800000},"content-version":"vor","delay-in-days":257,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>We investigate the stability of the functional equation 2<jats:italic>f<\/jats:italic>(<jats:italic>x<\/jats:italic> + <jats:italic>y<\/jats:italic>) + <jats:italic>f<\/jats:italic>(<jats:italic>x<\/jats:italic> \u2212 <jats:italic>y<\/jats:italic>) + <jats:italic>f<\/jats:italic>(<jats:italic>y<\/jats:italic> \u2212 <jats:italic>x<\/jats:italic>) \u2212 3<jats:italic>f<\/jats:italic>(<jats:italic>x<\/jats:italic>) \u2212 <jats:italic>f<\/jats:italic>(\u2212<jats:italic>x<\/jats:italic>) \u2212 3<jats:italic>f<\/jats:italic>(<jats:italic>y<\/jats:italic>) \u2212 <jats:italic>f<\/jats:italic>(\u2212<jats:italic>y<\/jats:italic>) = 0 by using the fixed point theory in the sense of  C\u0103dariu and  Radu.<\/jats:p>","DOI":"10.1155\/2011\/817079","type":"journal-article","created":{"date-parts":[[2011,9,16]],"date-time":"2011-09-16T02:04:25Z","timestamp":1316138665000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Fixed Point Approach to the Stability of the Cauchy Additive and Quadratic Type Functional Equation"],"prefix":"10.1155","volume":"2011","author":[{"given":"Sun Sook","family":"Jin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang-Hi","family":"Lee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2011,9,15]]},"reference":[{"key":"e_1_2_4_1_2","volume-title":"A collection of Mathematical Problems","author":"Ulam S. M.","year":"1968"},{"key":"e_1_2_4_2_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.27.4.222"},{"key":"e_1_2_4_3_2","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/00210064"},{"key":"e_1_2_4_4_2","doi-asserted-by":"publisher","DOI":"10.2307\/2042795"},{"key":"e_1_2_4_5_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1994.1211"},{"key":"e_1_2_4_6_2","first-page":"91","article-title":"A generalization of the Hyers-Ulam-Rassias stability of the Pexiderized quadratic equations. II","volume":"47","author":"Jun K.-W.","year":"2007","journal-title":"Kyungpook Mathematical Journal"},{"key":"e_1_2_4_7_2","doi-asserted-by":"publisher","DOI":"10.7153\/mia-04-25"},{"key":"e_1_2_4_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.11.053"},{"key":"e_1_2_4_9_2","doi-asserted-by":"publisher","DOI":"10.4134\/BKMS.2008.45.2.397"},{"key":"e_1_2_4_10_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1999.6546"},{"key":"e_1_2_4_11_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2000.6832"},{"key":"e_1_2_4_12_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002\u20109939\u201099\u201005156\u20104"},{"key":"e_1_2_4_13_2","article-title":"Fixed points and the stability of Jensen\u2032s functional equation","volume":"4","author":"C\u0103dariu L.","year":"2003","journal-title":"Journal of Inequalities in Pure and Applied Mathematics"},{"key":"e_1_2_4_14_2","series-title":"Grazer Mathematische Berichte","first-page":"43","volume-title":"Iteration Theory","author":"C\u0103dariu L.","year":"2004"},{"key":"e_1_2_4_15_2","first-page":"25","article-title":"Fixed points and the stability of quadratic functional equations","volume":"41","author":"C\u0103dariu L.","year":"2003","journal-title":"Analele Universit\u0103\u0163ii din Timi\u015foara"},{"key":"e_1_2_4_16_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002\u20109904\u20101968\u201011933\u20100"},{"key":"e_1_2_4_17_2","article-title":"Principles and applications of fixed point theory","author":"Rus I. A.","year":"1979","journal-title":"Editura Dacia, Cluj-Napoca"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2011\/817079.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2011\/817079.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2011\/817079","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,10]],"date-time":"2024-06-10T14:59:09Z","timestamp":1718031549000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2011\/817079"}},"subtitle":[],"editor":[{"given":"Yuri","family":"Sotskov","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2011,1]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["10.1155\/2011\/817079"],"URL":"https:\/\/doi.org\/10.1155\/2011\/817079","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,1]]},"assertion":[{"value":"2011-06-02","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-07-18","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-09-15","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"817079"}}