SUPERSTABILITY OF MULTIPLICATIVE LINEAR MAPPINGS
نویسندگان
چکیده
منابع مشابه
Superstability of Generalized Multiplicative Functionals
LetX be a set with a binary operation ◦ such that, for each x, y, z ∈ X, either x ◦y ◦z x ◦z ◦y, or z◦ x◦y x◦ z◦y . We show the superstability of the functional equation g x◦y g x g y . More explicitly, if ε ≥ 0 and f : X → C satisfies |f x ◦ y − f x f y | ≤ ε for each x, y ∈ X, then f x ◦ y f x f y for all x, y ∈ X, or |f x | ≤ 1 √1 4ε /2 for all x ∈ X. In the latter case, the constant 1 √ 1 4...
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The following note is a supplement to [1]. We will maintain the notation of [1] throughout, and all numbered items to which we refer are from that paper. Theorem 6.11 states that if M is a finitely generated R-module then Th(M,F) is stable. As pointed out in Remark 6.12, the proof Theorem 6.11 yields a stronger conclusion: Th(M,F) is superstable. These notes consist of detailed arguments for th...
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ژورنال
عنوان ژورنال: Communications of the Korean Mathematical Society
سال: 2011
ISSN: 1225-1763
DOI: 10.4134/ckms.2011.26.2.253