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- W2290761432 abstract "Abstract. In this article, we consider a modi ed quadratic func-tional equation and then investigate its generalized Hyers{Ulamstability theorem in quasi- -normed spaces. 1. IntroductionIn 1940, S.M. Ulam [17] raised the question concerning the stabilityof group homomorphisms: Let Gbe a group and let G 0 be a metricgroup with the metric d(; ). Given >0, does there exist a >0 suchthat if a mapping f: G!G 0 satis es the inequalityd(f(xy);f(x)f(y)) <for all x;y2G, then there exists a homomorphism F : G!G 0 withd(f(x);F(x)) <for all x2G? The case of approximately additivemappings was solved by D.H. Hyers [8] under the assumption that XandY are Banach spaces. A generalization of Hyers’ theorem was providedby Th.M. Rassias [12] in 1978 and by P. Gavruta [6] in 1994.We recall that the following functional equationf(x+ y) + f(x y) = 2[f(x) + f(y)]is called a quadratic functional equation which may be originated fromthe important parallelogram equality kx+yk 2 +kx yk" @default.
- W2290761432 created "2016-06-24" @default.
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- W2290761432 date "2015-05-15" @default.
- W2290761432 modified "2023-10-17" @default.
- W2290761432 title "APPROXIMATE QUADRATIC MAPPINGS IN QUASI-β-NORMED SPACES" @default.
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- W2290761432 doi "https://doi.org/10.14403/jcms.2015.28.2.311" @default.
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