共查询到20条相似文献,搜索用时 0 毫秒
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Jae-Young Chung 《Aequationes Mathematicae》2012,83(3):313-320
Let \mathbb R{\mathbb R} be the set of real numbers, f : \mathbb R ? \mathbb R{f : \mathbb {R} \to \mathbb {R}}, e 3 0{\epsilon \ge 0} and d > 0. We denote by {(x 1, y 1), (x 2, y 2), (x 3, y 3), . . .} a countable dense subset of \mathbb R2{\mathbb {R}^2} and let
$U_d:=\bigcup\nolimits_{j=1}^{\infty} \{(x, y)\in \mathbb {R}^2:\,|x|+|y| > d,\, |x-x_j| < 1,\, |y-y_j| < 2^{-j}\}.$U_d:=\bigcup\nolimits_{j=1}^{\infty} \{(x, y)\in \mathbb {R}^2:\,|x|+|y| > d,\, |x-x_j| < 1,\, |y-y_j| < 2^{-j}\}. 相似文献
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Marcin Balcerowski 《Aequationes Mathematicae》2018,92(2):201-209
We show connections between generalized versions of some conditional Cauchy equation and its basic form. As a consequence we obtain the solution of the generalized equations in some classes of regular functions. 相似文献
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Let R be the set of real numbers, Y a Banach space and f:R→Y. We prove the Hyers–Ulam stability theorem for the quadratic functional inequality
‖f(x+y)+f(x−y)−2f(x)−2f(y)‖≤? 5.
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Yu. L. Gaponenko 《Computational Mathematics and Modeling》1990,1(1):23-27
The paper investigates the stability of the Cauchy problem for the Laplace equation under the a priori assumption that the solution is bounded. A special metrization of the weak topology in the space L2 and the standard Fourier series technique are applied to obtain stability bounds for the solution of the Cauchy problem on the class of absolutely bounded functions.Translated from Vychislitel'naya Matematika i Matematicheskoe Obespechenie EVM, pp. 44–50, 1985. 相似文献
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Kil-Woung Jun 《Journal of Mathematical Analysis and Applications》2005,312(2):535-547
Let G1 be a vector space and G2 a Banach space. In this paper, we solve the generalized Hyers-Ulam-Rassias stability problem for a generalized form
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A. V. Kazeykina 《Computational Mathematics and Mathematical Physics》2010,50(4):690-710
The asymptotic behavior of the solution to the Cauchy problem for the Korteweg-de Vries-Burgers equation u
t
+ (f(u))
x
+ au
xxx
− bu
xx
= 0 as t → ∞ is analyzed. Sufficient conditions for the existence and local stability of a traveling-wave solution known in the case
of f(u) = u
2 are extended to the case of an arbitrary sufficiently smooth convex function f(u). 相似文献
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Valeriĭ A. Faĭziev Robert C. Powers Prasanna K. Sahoo 《Aequationes Mathematicae》2013,85(1-2):131-163
More than 33 years ago M. Kuczma and R. Ger posed the problem of solving the alternative Cauchy functional equation ${f(xy) - f(x) - f(y) \in \{ 0, 1\}}$ where ${f : S \to \mathbb{R}, S}$ is a group or a semigroup. In the case when the Cauchy functional equation is stable on S, a method for the construction of the solutions is known (see Forti in Abh Math Sem Univ Hamburg 57:215–226, 1987). It is well known that the Cauchy functional equation is not stable on the free semigroup generated by two elements. At the 44th ISFE in Louisville, USA, Professor G. L. Forti and R. Ger asked to solve this functional equation on a semigroup where the Cauchy functional equation is not stable. In this paper, we present the first result in this direction providing an answer to the problem of G. L. Forti and R. Ger. In particular, we determine the solutions ${f : H \to \mathbb{R}}$ of the alternative functional equation on a semigroup ${H = \langle a, b| a^2 = a, b^2 = b \rangle }$ where the Cauchy equation is not stable. 相似文献
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Béla Nagy 《Aequationes Mathematicae》1974,10(2-3):165-171
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章志飞 《高校应用数学学报(A辑)》2003,18(2):179-183
利用半群S(t)=e^—t(—∠←)θ/2=F^—1e—t^|ε|^0F的L^p-L^r估计,证明了修正Navier—Stokes方程解的存在性和惟一性。 相似文献
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