共查询到20条相似文献,搜索用时 15 毫秒
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Aequationes mathematicae - Roger Cuculière [Problem 11998, The American Mathematical Monthly 124 no. 7 (2017)] has posed the following problem: Find all continuous functions $$f: mathbb R... 相似文献
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László Losonczi 《Results in Mathematics》1996,29(3-4):305-310
Two stability results are proved. The first one states that Hosszú’s functional equation $$f(x+y-xy)+f(xy)=f(x)-f(y)=0\ \ \ \ \ (x,y \in \rm R)$$ is stable. The second is a local stability theorem for additive functions in a Banach space setting. 相似文献
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Henrik Stetkær 《Aequationes Mathematicae》2016,90(2):407-409
If \({f, g : G \to \mathbb{C}}\), f ≠ 0, is a solution of Wilson’s functional equation on a group G, then g is a d’Alembert function. 相似文献
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We give a classification of maximal subalgebras of rankn−1 for the extended Poincaré algebra
, which is realized on the set of solutions of the d'Alembert equation
. These subalgebras are used for constructing anzatses that reduce this equation to differential equations with two invariant
variables.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 6, pp. 651–662, June, 1994. 相似文献
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Jean-Luc Marichal 《Aequationes Mathematicae》2010,79(3):237-260
We investigate the n-variable real functions G that are solutions of the Chisini functional equation F(x) = F(G(x), . . . , G(x)), where F is a given function of n real variables. We provide necessary and sufficient conditions on F for the existence and uniqueness of solutions. When F is nondecreasing in each variable, we show in a constructive way that if a solution exists then a nondecreasing and idempotent
solution always exists. We also provide necessary and sufficient conditions on F for the existence of continuous solutions and we show how to construct such a solution. We finally discuss a few applications
of these results. 相似文献
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We prove that Euler’s equation , characterising homogeneous functions, is stable in Hyers–Ulam sense if and only if . 相似文献
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In this paper we find a closed form of the solution for the factored inhomogeneous linear equation
Under the hypothesis A
1, A
2, …, A
n
are infinitesimal generators of mutually commuting strongly continuous semigroups of bounded linear operators on a Banach
space X. Here we do not assume that A
j
s are distinct and we offer the computational method to get explicit solutions of certain partial differential equations. 相似文献
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