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- W2267128897 abstract "Using the notion of k-proper family we prove general results on the almost approximate stability of the polynomial functional equation. As one of the corollaries we obtain the generalization of the Theorem of R. Ger (cf. [4]): Theorem Let G be a uniquely n! divisible commutative semigroup and let I be a translation invariant proper ideal in G such that 1 i U ∈ I for every U ∈ I, i = 1, . . . , n. Let E be a Banach space. Then there for every e > 0 and every f : G → E satisfying ‖∆f(x, h)‖ ≤ e for Ω(I)-a.a. (x, h) ∈ G × G there exists a unique up to a constant function polynomial p : G → E of order n − 1 such that ‖f(x) − p(x)‖ ≤ 2(2 − 1)e for I-a.a. x ∈ G." @default.
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- W2267128897 date "2001-12-01" @default.
- W2267128897 modified "2023-09-23" @default.
- W2267128897 title "k-Proper families and almost approximately polynomial functions" @default.
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