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1.
Let P(z) be a polynomial of degree n with complex coefficients and consider the n–th order linear differential operator P(D). We show that the equation P(D)f = 0 has the Hyers–Ulam stability, if and only if the equation P(z) = 0 has no pure imaginary solution. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
2.
H. J. Munkholm obtained a generalization for topological manifolds of the famous Borsuk–Ulam type theorem proved by Conner and Floyd. The purpose of this paper is to prove a version of Conner and Floyd's theorem for generalized manifolds. 相似文献
3.
The specific heat of Fermi–Pasta–Ulam systems has until now been estimated through the energy fluctuations of a suitable subsystem, and opposite answers were apparently provided concerning its possible vanishing for vanishing temperatures. In the present paper a more realistic numerical implementation of the specific heat measurement is discussed, which mimics the interaction of the FPU system with a calorimeter. It is found that there exists a freezing critical temperature below which the relaxation times to equilibrium between FPU system and calorimeter become relevant, so that the system presents aging and hysteresis features very similar to those familiar in glasses and spin glasses. In particular, in the framework of such a point of view involving finite long times, the specific heat appears to vanish for vanishing temperatures. 相似文献
4.
The isovariant version of Borsuk–Ulam type theorems has been studied by Wasserman and the first author. In this paper, first we consider the relation between the existence of Cn-isovariant maps from free Cn-manifolds to representation spheres and Borsuk–Ulam type inequalities for their dimensions. Our main result classifies the Cn-isovariant maps by Cn-isovariant homotopy types when a Borsuk–Ulam type inequality holds. For proving it, we use the multidegree of a Cn-equivariant map developed by the first author. 相似文献
5.
In this paper, we first prove two existence and uniqueness results for fractional-order delay differential equation with respect to Chebyshev and Bielecki norms. Secondly, we prove the above equation is Ulam–Hyers–Mittag-Leffler stable on a compact interval. Finally, two examples are also provided to illustrate our results. 相似文献
6.
We obtain the infimum of the Hyers–Ulam stability constants for Stancu, Bernstein and Kantorovich operators and prove that in a class of certain positive linear operators this infimum for Bernstein operator has a minimality property. 相似文献
7.
John Michael Rassias Matina John Rassias 《Journal of Mathematical Analysis and Applications》2003,281(2):516-524
In 1941 Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 Bourgin was the second author to treat this problem for additive mappings. In 1982-1998 Rassias established the Hyers-Ulam stability of linear and nonlinear mappings. In 1983 Skof was the first author to solve the same problem on a restricted domain. In 1998 Jung investigated the Hyers-Ulam stability of more general mappings on restricted domains. In this paper we introduce additive mappings of two forms: of “Jensen” and “Jensen type,” and achieve the Ulam stability of these mappings on restricted domains. Finally, we apply our results to the asymptotic behavior of the functional equations of these types. 相似文献
8.
Hark-Mahn Kim John Michael Rassias 《Journal of Mathematical Analysis and Applications》2007,336(1):277-296
In 1968 S.M. Ulam proposed the problem: “When is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true?” In 1978 P.M. Gruber proposed the Ulam type problem: “Suppose a mathematical object satisfies a certain property approximately. Is it then possible to approximate this object by objects, satisfying the property exactly?” In this paper we solve the generalized Ulam stability problem for non-linear Euler-Lagrange quadratic mappings satisfying approximately a mean equation and an Euler-Lagrange type functional equations in quasi-Banach spaces and p-Banach spaces. 相似文献
9.
Churong Chen Martin Bohner Baoguo Jia 《Mathematical Methods in the Applied Sciences》2019,42(18):7461-7470
We study the Ulam‐Hyers stability of linear and nonlinear nabla fractional Caputo difference equations on finite intervals. Our main tool used is a recently established generalized Gronwall inequality, which allows us to give some Ulam‐Hyers stability results of discrete fractional Caputo equations. We present two examples to illustrate our main results. 相似文献
10.
John Michael Rassias 《Journal of Mathematical Analysis and Applications》2002,276(2):747-762
In 1941 D.H. Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 D.G. Bourgin was the second author to treat the Ulam problem for additive mappings. In 1982-1998 we established the Hyers-Ulam stability for the Ulam problem of linear and nonlinear mappings. In 1983 F. Skof was the first author to solve the Ulam problem for additive mappings on a restricted domain. In 1998 S.M. Jung investigated the Hyers-Ulam stability of additive and quadratic mappings on restricted domains. In this paper we improve the bounds and thus the results obtained by S.M. Jung, in 1998. Besides we establish the Ulam stability of mixed type mappings on restricted domains. Finally, we apply our recent results to the asymptotic behavior of functional equations of different types. 相似文献