共查询到20条相似文献,搜索用时 950 毫秒
1.
We prove generalized Hyers-Ulam–Rassias stability of the cubic functional equation f(kx+y)+f(kx?y)=k[f(x+y)+f(x?y)]+2(k 3?k)f(x) for all \(k\in \Bbb{N}\) and the quartic functional equation f(kx+y)+f(kx?y)=k 2[f(x+y)+f(x?y)]+2k 2(k 2?1)f(x)?2(k 2?1)f(y) for all \(k\in \Bbb{N}\) in non-Archimedean normed spaces. 相似文献
2.
We construct a family of relativistic-invariant generating functionasl of the form
F(f* ,g) = exp{ gò\fracdkw(k) f* (k)g(k) }F(f^* ,g) = \exp \left\{ {\gamma \int {\frac{{dk}}{{w(k)}}} f^* (k)g(k)} \right\} 相似文献
3.
We prove that, given a sequence {ak}k=1∞ with ak ↓ 0 and {ak}k=1∞ ? l2, reals 0 < ε < 1 and p ∈ [1, 2], and f ∈ Lp(0, 1), we can find f ∈ Lp(0, 1) with mes{f ≠ f < ε whose nonzero Fourier–Walsh coefficients ck(f) are such that |ck(f)| = ak for k ∈ spec(f). 相似文献
4.
Geno Nikolov 《Numerische Mathematik》1992,62(1):557-565
Summary LetI(f)L(f)=
k=0
r
=0
vk–1
a
k
f
()(X
k
) be a quadrature formula, and let {S
n
(f)}
n=1
be successive approximations of the definite integralI(f)=
0
1
f(x)dx obtained by the composition ofL, i.e.,S
n(f)=L(
n
), where
.We prove sufficient conditions for monotonicity of the sequence {S
n
(f)}
n=1
. As particular cases the monotonicity of well-known Newton-Cotes and Gauss quadratures is shown. Finally, a recovery theorem based on the monotonicity results is presented 相似文献
5.
N. Temirgaliev 《Mathematical Notes》1976,20(6):1026-1030
For any sequence {Nk} with {Nk} O we find sharp theorems on the inclusion of the classes {f: f l (0, 2),e
k
(1)
(f) = O(Nk)¦, whereE
k
(1)
(f) is the best approximation (in L) of f by trigonometric polynomials of order no greater than k, in the classL
with slowly growing and in the class Lv, 1 <v < .Translated from Matematicheskie Zametki, Vol. 20, No. 6, pp. 835–841, December, 1976. 相似文献
6.
LetF(W) be a Wiener functional defined byF(W)=I
n(f) whereI
n(f) denotes the multiple Wiener-Ito integral of ordern of the symmetricL
2([0, 1]
n
) kernelf. We show that a necessary and sufficient condition for the existence of a continuous extension ofF, i.e. the existence of a function ø(·) from the continuous functions on [0, 1] which are zero at zero to which is continuous in the supremum norms and for which ø(W)=F(W) a.s, is that there exists a multimeasure (dt
1,...,dt
n
) on [0, 1]
n
such thatf(t
1, ...,t
n
) = ((t
1, 1]), ..., (t
n
, 1]) a.e. Lebesgue on [0, 1]
n
. Recall that a multimeasure (A
1,...,A
n
) is for every fixedi and every fixedA
i,...,Ai-1, Ai+1,...,An a signed measure inA
i
and there exists multimeasures which are not measures. It is, furthermore, shown that iff(t
1,t
2, ...,t
n
) = ((t
1, 1], ..., (t
n
, 1]) then all the tracesf
(k),
off exist, eachf(k) induces ann–2k multimeasure denoted by (k), the following relation holds
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