{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:36:40Z","timestamp":1753886200517,"version":"3.41.2"},"reference-count":42,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,12,6]],"date-time":"2011-12-06T00:00:00Z","timestamp":1323129600000},"content-version":"vor","delay-in-days":339,"URL":"https:\/\/linproxy.fan.workers.dev:443\/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>Let <jats:italic>A<\/jats:italic> be an algebra, and let <jats:italic>\u03b8<\/jats:italic>, <jats:italic>\u03d5<\/jats:italic> be ring automorphisms of <jats:italic>A<\/jats:italic>. An additive\nmapping <jats:italic>H<\/jats:italic> : <jats:italic>A<\/jats:italic> \u2192 <jats:italic>A<\/jats:italic> is called a (<jats:italic>\u03b8<\/jats:italic>, <jats:italic>\u03d5<\/jats:italic>)\u2010derivation if <jats:italic>H<\/jats:italic>(<jats:italic>x<\/jats:italic><jats:italic>y<\/jats:italic>) = <jats:italic>H<\/jats:italic>(<jats:italic>x<\/jats:italic>)<jats:italic>\u03b8<\/jats:italic>(<jats:italic>y<\/jats:italic>) + <jats:italic>\u03d5<\/jats:italic>(<jats:italic>x<\/jats:italic>)<jats:italic>H<\/jats:italic>(<jats:italic>y<\/jats:italic>) for all <jats:italic>x<\/jats:italic>, <jats:italic>y<\/jats:italic> \u2208 <jats:italic>A<\/jats:italic>. Moreover, an additive mapping <jats:italic>F<\/jats:italic> : <jats:italic>A<\/jats:italic> \u2192 <jats:italic>A<\/jats:italic> is said to be a generalized (<jats:italic>\u03b8<\/jats:italic>, <jats:italic>\u03d5<\/jats:italic>)\u2010derivation if there exists a (<jats:italic>\u03b8<\/jats:italic>, <jats:italic>\u03d5<\/jats:italic>)\u2010derivation <jats:italic>H<\/jats:italic> : <jats:italic>A<\/jats:italic> \u2192 <jats:italic>A<\/jats:italic> such that <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>)<jats:italic>\u03b8<\/jats:italic>(<jats:italic>y<\/jats:italic>) + <jats:italic>\u03d5<\/jats:italic>(<jats:italic>x<\/jats:italic>)<jats:italic>H<\/jats:italic>(<jats:italic>y<\/jats:italic>) for all <jats:italic>x<\/jats:italic>, <jats:italic>y<\/jats:italic> \u2208 <jats:italic>A<\/jats:italic>. In this paper, we investigate the superstability of generalized (<jats:italic>\u03b8<\/jats:italic>, <jats:italic>\u03d5<\/jats:italic>)\u2010derivations in non\u2010Archimedean algebras by using a version of fixed point theorem via Cauchy\u2019s functional equation.<\/jats:p>","DOI":"10.1155\/2011\/726020","type":"journal-article","created":{"date-parts":[[2011,12,6]],"date-time":"2011-12-06T21:10:34Z","timestamp":1323205834000},"update-policy":"https:\/\/linproxy.fan.workers.dev:443\/https\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Stability and Superstability of Generalized (<i>\u03b8<\/i>, <i>\u03d5<\/i>)\u2010Derivations in Non\u2010Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation"],"prefix":"10.1155","volume":"2011","author":[{"given":"M. Eshaghi","family":"Gordji","sequence":"first","affiliation":[]},{"given":"M. B.","family":"Ghaemi","sequence":"additional","affiliation":[]},{"given":"G. 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