Titlebook: Stability of Functional Equations in Several Variables; Donald H. Hyers,George Isac,Themistocles M. Rassia Book 1998 Springer Science+Busi

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Progress in Nonlinear Differential Equations and Their Applicationshttp://image.papertrans.cn/s/image/875340.jpg

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Generalizations. The Method of Invariant Means,As was seen above in Corollary 1.2, there is no difficulty in generalizing Theorem 1.1 to mappings from a commutative semigroup . to a Banach space. We note here that the property of commutativity was used only in demonstrating the additivity of the mapping ..

引起

Functions with Bounded ,th Differences,Let . be a commutative semigroup with a zero element and . a real Banach space. For functions ., we define the difference operator △. . (.)by △. . (.). (.) . (.). Similarly, we define.Note that the nth difference is symmetric in the increments ..,., ... When all the increments are equal to . we write.instead of..

注意

Functional Congruences,In the following we consider a mapping ., where . is a real topological vector space, such that.for all . in ..

出價(jià)

978-1-4612-7284-7Springer Science+Business Media New York 1998

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Stability of Functional Equations in Several Variables978-1-4612-1790-9Series ISSN 1421-1750 Series E-ISSN 2374-0280

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來(lái)這真柔軟

Approximately Multiplicative Mappings. Superstability, function from a real vector space . to the real numbers satisfying |. (.) . (.) . (.) | < . for some fixed . 0 and all ., . in ., then . is either bounded or else . (. y) = . (.). (.) for all .,. in ..