Results 11 to 20 of about 151,638 (261)
On a system of functional equations
Aequationes Mathematicae, 1985 Motivated by the theory of generalized Appel sequences when looking for the square roots of the Laguerre sequence, the authors study the system of functional equations (1) \(H(H(t))=t/(t-1)\); (2) \(G(t)G(H(t))=(1- t)^{-\alpha -1}\), \(\alpha >-1\), in the class of formal power series (3) \(H(t)=\sum^{\infty}_{k=1}h_ kt^ k\), \(G(t)=\sum^{\infty}_{k=0 ...
Kuczma, Marek, Choczewski, Bogdan
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On extension of solutions of a simultaneous system of iterative functional equations [PDF]
Opuscula Mathematica, 2009 Some sufficient conditions which allow to extend every local solution of a simultaneous system of equations in a single variable of the form \[ \varphi(x) = h (x, \varphi[f_1(x)],\ldots,\varphi[f_m(x)]),\] \[\varphi(x) = H (x, \varphi[F_1(x)],\ldots ...
Janusz Matkowski
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Stability results for the functional differential equations associated to water hammer in hydraulics
Electronic Journal of Qualitative Theory of Differential Equations, 2022 There is considered a system of two sets of partial differential equations describing the water hammer in a hydroelectric power plant containing the dynamics of the tunnel, turbine penstock, surge tank and hydraulic turbine.
Vladimir Rasvan
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CANONICAL APPROXIMATIONS IN IMPULSE STABILIZATION FOR A SYSTEM WITH AFTEREFFECT
Ural Mathematical Journal, 2023 For optimal stabilization of an autonomous linear system of differential equations with aftereffect and impulse controls, the formulation of the problem in the functional state space is used.
Yuri F. Dolgii
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016 This paper deals with the existence, uniqueness and iterative approximations of solutions for the functional equations and system of functional equations arising in dynamic programming of multistage decision making processes in Banach spaces and complete
Deepmala, Agarwal Ravi P.
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On systems of linear functional equations
Aequationes Mathematicae, 1982 The square functional equation \[ (1)\quad f(x+t,y+t)+f(x+t,y-t)+f(x-t,y- t)+f(x-t,y+t)=4f(x,y), \] where f: \(R\times R\to R\) and x, y, t are real variables, was investigated by \textit{J. Acźel}, the reviewer, \textit{M. A. McKiernan} and \textit{G.N. Sakovič} [ibid. 1, 37-53 (1968; Zbl 0157.461)].
Laird, P.G., Mills, J.
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Karpatsʹkì Matematičnì Publìkacìï, 2013 The article shows that the system of the functional equations $S(x+y)=S(x)C(y)+S(y)C(x),\,C(x+y)=C(x)C(y)-S(y)S(x)$ denes a broader class of the functions than the trigonometric equations.
Е. V. Velichko, I. G. Tkachenko
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Functional Equations and Poincaré Invariant Mechanical Systems
SIAM Journal on Mathematical Analysis, 2002 We study the following functional equation that has arisen in the context of mechanical systems invariant under the Poincare algebra: \sum\limits_{i=1}^{n+1}\dfrac{\partial}{\partial x_{i}}\prod\limits_{j\neq i}f(x_{i}-x_{j}) =0,\qquad n \geq 2. New techniques are developed and the general solution within a certain class of functions is given.
John G. B. Byatt-Smith, Harry W. Braden
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Weak Solutions of a Coupled System of Urysohn-Stieltjes Functional (Delayed) Integral Equations
Complexity, 2018 We study the existence of weak solutions for the coupled system of functional integral equations of Urysohn-Stieltjes type in the reflexive Banach space E.
A. M. A. El-Sayed, M. M. A. Al-Fadel
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On the Asymptotic Equivalence of Ordinary and Functional Stochastic Differential Equations
Journal of Optimization, Differential Equations and Their Applications, 2023 This paper studies the asymptotic behavior of solutions of linear stochastic functional-differential equations. This behavior is investigated using the method of asymptotic equivalence, according to which an ordinary system of linear differential ...
Olexandr M. Stanzhytskyi +2 more
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