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Functional equations in the theory of dynamic programming. XV. Layered functionals and partial differential equations

, 1969
Richard Bellman
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Functionals on the Space of Solutions to a Differential Equation with Constant Coefficients. The Fourier and Borel Transformations.

, 1968
Christer O. Kiselman
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On alternative functional equations

Aequationes Mathematicae, 1976
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On a functional equation for characteristic functions [PDF]

Applicationes Mathematicae, 1983
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On a ‘cube functional equation’

Aequationes Mathematicae, 1969
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Alternative problems for nonlinear functional equations

, 1968
Stephen Bancroft, Jack K. Hale, Daniel Sweet   +2 more
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On an alternative functional equation

Aequationes Mathematicae, 1976
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A stochastic functional equation

Aequationes Mathematicae, 1976
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On a functional equation

Mathematical Proceedings of the Cambridge Philosophical Society, 1965
Introduction. The object of this note is to give a proof of the following theorem on the solution of an important functional equation.
A. R. Reddy, C. T. Rajagopal
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Functional Equations and Distribution Functions

Results in Mathematics, 1994
Let \(a \in (0,1)\), \(N \in \mathbb{N} \backslash \{1\}\) and \(- 1 = \beta_0 \leq \beta_1 \leq \dots \leq \beta_{N - 1} = 1\). Then the functional equation \[ f(x) = {1 \over N} \sum^{N - 1}_{k = 0} f \left( {x - \beta_k \over a} \right) \] has a unique bounded solution \(f : \mathbb{R} \to \mathbb{R}\) vanishing on \((- \infty, -1/(1 - a))\) and ...
Borwein, Jonathan M., Girgensohn, Roland
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