共查询到20条相似文献，搜索用时 31 毫秒
1.
Mohammad Sal Moslehian 《Bulletin of the Brazilian Mathematical Society》2007,38(4):611-622
In this paper, we establish the generalized Hyers–Ulam–Rassias stability of C*-ternary ring homomorphisms associated to the Trif functional equation
相似文献
2.
Fridoun Moradlou Hamid Vaezi G. Zamani Eskandani 《Mediterranean Journal of Mathematics》2009,6(2):233-248
In this paper we establish the general solution of the functional equation
and investigate the Hyers–Ulam–Rassias stability of this equation in quasi-Banach spaces. The concept of Hyers–Ulam–Rassias
stability originated from Th. M. Rassias’ stability theorem that appeared in his paper: On the stability of the linear mapping
in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300.
相似文献
3.
Kil-Woung JUN Hark-Mahn KIM 《数学学报(英文版)》2006,22(6):1781-1788
In this paper, we establish the general solution and the generalized Hyers-Ulam-Rassias stability problem for a cubic Jensen-type functional equation,4f（（3x＋y）/4）＋4f（（x＋3y）/4）=6f（（x＋y）/2）＋f（x）＋f（y）,9f（（2x＋y/3）＋9f（（x＋2y）/3）=16f（（x＋y）/2＋f（x）＋f（y）in the spirit of D. H. Hyers, S. M. Ulam, Th. M. Rassias and P. Gaevruta. 相似文献
4.
Choonkil PARK Jian Lian CUI 《数学学报(英文版)》2007,23(11):1919-1936
Let X and Y be vector spaces. The authors show that a mapping f ： X →Y satisfies the functional equation 2d f（∑^2d j=1（-1）^j＋1xj/2d）=∑^2dj=1（-1）^j＋1f（xj） with f（0） = 0 if and only if the mapping f ： X→ Y is Cauchy additive, and prove the stability of the functional equation （≠） in Banach modules over a unital C^＊-algebra, and in Poisson Banach modules over a unital Poisson C＊-algebra. Let A and B be unital C^＊-algebras, Poisson C^＊-algebras or Poisson JC^＊- algebras. As an application, the authors show that every almost homomorphism h ： A →B of A into is a homomorphism when h（（2d-1）^nuy） =- h（（2d-1）^nu）h（y） or h（（2d-1）^nuoy） = h（（2d-1）^nu）oh（y） for all unitaries u ∈A, all y ∈ A, n = 0, 1, 2,....
Moreover, the authors prove the stability of homomorphisms in C^＊-algebras, Poisson C^＊-algebras or Poisson JC^＊-algebras. 相似文献
5.
Choonkil BAAK 《数学学报(英文版)》2006,22(6):1789-1796
Let X, Y be vector spaces. It is shown that if a mapping f ： X → Y satisfies f（（x＋y）/2＋z）＋f（（x-y）/2＋z=f（x）＋2f（z）,（0.1） f（（x＋y）/2＋z）-f（（x-y）/2＋z）f（y）,（0.2） or 2f（（x＋y）/2＋x）=f（x）＋f（y）＋2f（z）（0.3）for all x, y, z ∈ X, then the mapping f ： X →Y is Cauchy additive.
Furthermore, we prove the Cauchy-Rassias stability of the functional equations （0.1）, （0.2） and （0.3） in Banach spaces. The results are applied to investigate isomorphisms between unital Banach algebras. 相似文献
6.
In this paper, we establish the generalized Hyers–Ulam–Rassias stability of homomorphisms between ternary algebras associated
to the generalized Jensen functional equation
. 相似文献
7.
We prove the following statement.
Let , and let . Suppose that, for all and , the sequence satisfies the relation
where e(u) : = e2πiu
.
Then
where
q is the set of q-multiplicative functions g such that . 相似文献
8.
For 0 < α < mn and nonnegative integers n ≥ 2, m ≥ 1, the multilinear fractional integral is defined by
where = (y
1,y
2, ···, y
m
) and denotes the m-tuple (f
1,f
2, ···, f
m
). In this note, the one-weighted and two-weighted boundedness on L
p
(ℝ
n
) space for multilinear fractional integral operator I
α(m) and the fractional multi-sublinear maximal operator M
α(m) are established respectively. The authors also obtain two-weighted weak type estimate for the operator M
α(m).
Supported in Part by the NNSF of China under Grant #10771110, and by NSF of Ningbo City under Grant #2006A610090. 相似文献
9.
We use an inequality due to Bochnak and Lojasiewicz, which follows from the Curve Selection Lemma of real algebraic geometry
in order to prove that, given a C
r
function , we have
where . This shows that the so-called Morse decomposition of the critical set, used in the classical proof of the Morse–Sard theorem, is not necessary: the conclusion of the Morse
decomposition lemma holds for the whole critical set. We use this result to give a simple proof of the classical Morse–Sard
theorem (with sharp differentiability assumptions). 相似文献
10.
Let A be a compact set in of Hausdorff dimension d. For s ∈ (0,d) the Riesz s-equilibrium measure μ
s
is the unique Borel probability measure with support in A that minimizes
over all such probability measures. If A is strongly -rectifiable, then μ
s
converges in the weak-star topology to normalized d-dimensional Hausdorff measure restricted to A as s approaches d from below.
This research was supported, in part, by the U. S. National Science Foundation under grants DMS-0505756 and DMS-0808093. 相似文献
11.
<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-invariants of Riemannian foliations
Luis Sanguiao 《Annals of Global Analysis and Geometry》2008,33(3):271-292
For a Riemannian foliation on a closed manifold M, we define L
2-spectral sequence Betti numbers and spectral sequence Novikov–Shubin invariants. The spectral sequence of the lift of to the universal covering of M is used in the definitions. These invariants are natural extensions of the L
2-Betti numbers and the Novikov–Shubin invariants of differentiable manifolds. It is shown that these numbers are invariant
by foliated homotopy equivalences, and they are computed for several examples.
相似文献
12.
Wen-Bin Zhang 《Mathematische Zeitschrift》2009,261(1):233-234
Let be the generalized integers n
j
associated with a set of generalized primes p
i
in Beurling’s sense. On the basis of the general mean-value theorems, established in our previous work, for multiplicative
function f(n
j
) defined on , we prove extensions, in functional form and in mean-value form, of the Elliott–Daboussi theorem to high order mean-values.
For the main result, let α,ρ, and τ be positive real constants such that α > 1,ρ≥1 and . Then a multiplicative function f satisfies the following conditions, with some constant , (1) All four series
converge and (2)
if and only if the order τρ mean-value
exists with and the limit
exists with . The proof is deduced from an intrinsic connection between m
f
and .
An erratum to this article can be found at 相似文献
13.
Multivariate Refinement Equations and Convergence of Cascade Algorithms in Lp（0〈p〈1）Spaces 总被引：1，自引：0，他引：1
SongLI 《数学学报(英文版)》2003,19(1):97-106
We consider the solutions of refinement equations written in the form
where the vector of functions ϕ = (ϕ
1, ..., ϕ
r
)
T
is unknown, g is a given vector of compactly supported functions on ℝ
s
, a is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s dilation matrix with m = |detM|. Inhomogeneous refinement equations appear in the construction of multiwavelets and the constructions of wavelets on a finite
interval. The cascade algorithm with mask a, g, and dilation M generates a sequence ϕ
n
, n = 1, 2, ..., by the iterative process
from a starting vector of function ϕ
0. We characterize the L
p
-convergence (0 < p < 1) of the cascade algorithm in terms of the p-norm joint spectral radius of a collection of linear operators associated with the refinement mask. We also obtain a smoothness
property of the solutions of the refinement equations associated with the homogeneous refinement equation.
This project is supported by the NSF of China under Grant No. 10071071 相似文献
14.
In this paper, we prove the Hyers-Ulam-Rassias stability of isometric homomorphisms in proper CQ＊-algebras for the following Cauchy-Jensen additive mapping： 2f[（x1＋x2）/2＋y]=f（x1）＋f（x2）＋2f（y） The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias＇ stability theorem that appeared in the paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 （1978）, 297-300. This is applied to investigate isometric isomorphisms between proper CQ＊-algebras. 相似文献
15.
YunYanYANG 《数学学报(英文版)》2003,19(1):63-68
In this paper,we derive an elementary identity for smooth solutions of the following equation:△u(x) K(x)e^2u(x)=0 in R^2 and use it to get some global properties of the solutions. 相似文献
16.
ChunGilPARK 《数学学报(英文版)》2004,20(6):1047-1056
In this paper, we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen‘s equations in Banach modules over a unital C^*-algebra. It is applied to show the stability of universal Jensen‘s equations in a Hilbert module over a unital C^*-algebra. Moreover, we prove the stability of linear operators in a Hilbert module over a unital C^*-algebra. 相似文献
17.
In this paper we establish results on the existence of nontangential limits for weighted
-harmonic functions in the weighted Sobolev space
, for some q>1 and w in the Muckenhoupt A
q
class, where
is the unit ball in
. These results generalize the ones in Sect. 3 of Koskela et al., Trans. Am. Math. Soc. 348(2), 755–766, 1996, where the weight was identically equal to one. Weighted
-harmonic functions are weak solutions of the partial differential equation
where
for some fixed q∈(1,∞), where 0<α≤β<∞, and w(x) is a q-admissible weight as in Chap. 1 of Heinonen et al., Nonlinear Potential Theory, 2006.
Later, we apply these results to improve on results of Koskela et al., Trans. Am. Math. Soc. 348(2), 755–766, 1996 and Martio and Srebro, Math. Scand. 85, 49–70, 1999 on the existence of radial limits for bounded quasiregular mappings in the unit ball of
with some growth restriction on their multiplicity function.
相似文献
18.
Let n,p and k be three non negative integers. We prove that the apparently rational fractions of q:
are actually polynomials of q with non negative integer coefficients. This generalizes a recent result of Lassalle (Ann. Comb. 6(3–4), 399–405, 2002),
in the same way as the classical q-binomial coefficients refine the ordinary binomial coefficients.
相似文献
19.
In the present paper, the following Dirichlet problem and Neumann problem involving the p-Laplacian
and
are studied and some new multiplicity results of solutions for systems (1.λ) and (2.λ) are obtained. Moreover, by using the
KKM principle we give also two new existence results of solutions for systems (1.1) and (2.1).
This Work is supported in part by the National Natural Science Foundation of China (10561011). 相似文献
| ((1.λ)) |
| ((2.λ)) |
20.
Hui Yin Shuyue Chen Jing Jin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(6):969-1001
This paper is concerned with the large time behavior of traveling wave solutions to the Cauchy problem of generalized Benjamin–Bona–Mahony–Burgers
equations
with prescribed initial data
Here v( > 0), β are constants, u
± are two given constants satisfying u
+ ≠ u
− and the nonlinear function f(u) ∈C
2(R) is assumed to be either convex or concave. An algebraic time decay rate to traveling waves of the solutions of the Cauchy
problem of generalized Benjamin-Bona-Mahony-Burgers equation is obtained by employing the weighted energy method developed
by Kawashima and Matsumura in [6] to discuss the asymptotic behavior of traveling wave solutions to the Burgers equation.
revised: May 23 and August 8, 2007 相似文献