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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 describe the set of solutions of Wilsons functional equation on any
step 2 nilpotent group and how the set of classical solutions
in certain cases must be supplemented by 4-dimensional spaces of
solutions. 相似文献
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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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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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Prondanai Kaskasem Chakkrid Klin-eam Yeol Je Cho 《Journal of Fixed Point Theory and Applications》2018,20(2):76
In this paper, we prove the Hyers–Ulam–Rassias stability of the generalized Cauchy–Jensen set-valued functional equation defined by for all \(x,y,z \in X\) and \(\alpha \ge 2\) on a Banach space by using the fixed point alternative theorem.
相似文献
$$\begin{aligned} \alpha f\left( \frac{x+y}{\alpha } + z\right) = f(x) \oplus f(y)\oplus \alpha f(z) \end{aligned}$$
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Kazuki Okamura 《Aequationes Mathematicae》2016,90(6):1071-1085
We consider regularity for solutions of a class of de Rham’s functional equations. Under some smoothness conditions of functions making up the equation, we improve some results in Hata (Japan J Appl Math 2:381–414, 1985). Our results are applicable to some cases when the functions making up the equation are non-linear functions on an interval, specifically, polynomials and linear fractional transformations. Our results imply the singularity of some well-known singular functions, in particular, Minkowski’s question-mark function, and, some small perturbed functions of the singular functions. 相似文献
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We study generalizations of the Darcy, Forchheimer, Brinkman and Stokes problem in which the viscosity and the drag coefficient depend on the shear rate and the pressure. We focus on existence of weak solutions to the problem, with the chief aim to capture as wide a group of viscosities and drag coefficients as mathematically feasible and to provide a theory that holds under minimal, not very restrictive conditions. Even in the case of generalized Stokes system, the established result answers a question on existence of weak solutions that has been open so far. 相似文献
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