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Cantor Sets and Integral-Functional Equations
Zeitschrift für Analysis und ihre Anwendungen, 1998In this paper, we continue our considerations in [1] on a homogeneous integral-functional equation with a parameter a > 1 . In the case of a > 2 the solution
Berg, L., Krüppel, M.
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Integral Equations for the Schrödinger Wave Function
American Journal of Physics, 1959For many problems in quantum mechanics it proves to be useful to write the Schrödinger equation as an integral equation rather than as a differential equation. In this paper we describe how the transformation of the Schrödinger equation from differential form to integral form may be accomplished.
Tobocman, W., Foldy, L. L.
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A note on an integrated cauchy functional equation
Acta Mathematicae Applicatae Sinica, 1989The following equation \(f(x)=\int^{\infty}_{0}f(x+y)d\mu (y),\quad a.e.\quad x\geq 0,\) where \(\mu\) is a positive regular Borel measure defined in (0,\(\infty)\), called an integrated Cauchy functional equation, is discussed in order to establish its relevant nonnegative locally integrable solutions in (0,\(\infty)\).
Lau, Kasing, Gu, Huamin
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On a functional-integral equation with deviating arguments
Applied Mathematics and Computation, 20140 ...
Mohamed Abdalla Darwish +2 more
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Integral Equations and Functionals
Mathematics Magazine, 1950Introduction. It would be difficult to think of any two topics in mathematical analysis more central and more widely studied during the last fifty years than the theory of integral equations and functionals. Here we are using the word functional as a noun and not as an adjective.
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Integrable solutions of a functional equation related to Wilson's equation
Publicationes Mathematicae Debrecen, 2003The authors study for \(a>0\) and \(b>0\) the functional equation \[ af(x)+bf(y)=f(ax+by)g(y-x),\qquad x,y\in \mathbb R, \] where the functions \(f,g:\mathbb R\to \mathbb R\) are assumed to be locally integrable and continuous at the origin, respectively. They find the solutions under various assumptions on \(f(0)\) and \(g(0)\) and the derivatives of \
Choczewski, B., Powązka, Z.
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Integrable solutions of a functional-integral equation
1992A theorem about the existence of solutions of the functional-integral equation (1) \(x(t)=f\left(t,\int^ 1_ 0k(t,s)g(s,x(s))ds\right)\), \(t\in[0,1]\), is proved. The technique used in the proof depends on an interesting conjunction of the notions of the measure of weak noncompactness and the Schauder fixed point principle. It is worth while to mention
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Integral and functional equations
1960An equation for a function u (x 1, x 2, ..., x n ) of n independent variables x 1, x 2, ..., x n , in the simplest case for a function y(x), is called an integral equation when it involves an integral with the function u appearing in its integrand and with at least one of the arguments of u among its variables of integration.
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1999
Let X be an arbitrary Banach space with the norm ∥·∥. We denote the Euclidean norm in R n and the norm in the Banach space X by the same symbol. Elements of the space R n will be denoted by x = (x1, …, x n ), s = (s1, …, s n ). Let E ⊂ R + n be a compact set and G(x) = }ξ ∈ E:ξ≤x}. Assume that functions $$ E \in C\left( {E \times {X^m} \times X,\,X}
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Let X be an arbitrary Banach space with the norm ∥·∥. We denote the Euclidean norm in R n and the norm in the Banach space X by the same symbol. Elements of the space R n will be denoted by x = (x1, …, x n ), s = (s1, …, s n ). Let E ⊂ R + n be a compact set and G(x) = }ξ ∈ E:ξ≤x}. Assume that functions $$ E \in C\left( {E \times {X^m} \times X,\,X}
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Functional integral via functional equation
Letters in Mathematical Physics, 1994zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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