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Given a probability space (Ω,,P) and a subset X of a normed space we consider functions f:X × Ω → X and investigate the speed of convergence of the sequence (fⁿ(x,·)) of the iterates $f ⁿ : X \times Ω^{ℕ} \to X$ defined by f¹(x,ω ) = f(x,ω₁), $f^{n + 1} (x, ω) = f (f ⁿ (x, ω), ω_{n + 1})$ .

On the critical values of parametric resonance in Meissner's equation by the method of difference equations.

Hatvani, László (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

On the Definition of a Quadratic Form

Svetozar Kurepa (1987)

Publications de l'Institut Mathématique

On the dependence of the continous solutions of a functional equation on an arbitrary function.

Cz. Dyjak (1975)

Publications de l'Institut Mathématique [Elektronische Ressource]

On The Dependence Of The Continuous Solutions Of A Functional Equation On An Arbitrary Function

Czeslaw Dyjak (1975)

Publications de l'Institut Mathématique

On the determination of strict t-norms on some diagonal segments.

J.P. Bézivin, M.S. Tomás (1993)

Aequationes mathematicae

On the difference equation $x_{n + 1} = \frac{a_{0} x_{n} + a_{1} x_{n - 1} + \dots + a_{k} x_{n - k}}{b_{0} x_{n} + b_{1} x_{n - 1} + \dots + b_{k} x_{n - k}}$

Elmetwally M. Elabbasy, Hamdy El-Metwally, E. M. Elsayed (2008)

Mathematica Bohemica

In this paper we investigate the global convergence result, boundedness and periodicity of solutions of the recursive sequence $x_{n + 1} = \frac{a_{0} x_{n} + a_{1} x_{n - 1} + \dots + a_{k} x_{n - k}}{b_{0} x_{n} + b_{1} x_{n - 1} + \dots + b_{k} x_{n - k}}, n = 0, 1, \dots$ where the parameters $a_{i}$ and $b_{i}$ for $i = 0, 1, \dots, k$ are positive real numbers and the initial conditions $x_{- k}, x_{- k + 1}, \dots, x_{0}$ are arbitrary positive numbers.

On the difference equation $x_{n + 1} = a x_{n} - b x_{n} / (c x_{n} - d x_{n - 1})$ .

Elabbasy, E.M., El-Metwally, H., Elsayed, E.M. (2006)

Advances in Difference Equations [electronic only]

On the difference equation $x_{n + 1} = \sum_{j = 0}^{k} a_{j} f_{j} (x_{n - j})$ .

Stević, Stevo (2007)

Discrete Dynamics in Nature and Society

On the difference equation $x_{n + 1} = x_{n} x_{n - 2} - 1$ .

Kent, Candace M., Kosmala, Witold, Stević, Stevo (2011)

Abstract and Applied Analysis

On the difference equation $x_{n + 1} = α + x_{n - m} / x_{n}^{k}$ .

Yalçinkaya, İbrahim (2008)

Discrete Dynamics in Nature and Society

On the difference equation $x_{n + 1} = (α x_{n} + β x_{n - 1}) e^{- x_{n}}$ .

Ding, Xiaohua, Zhang, Rongyan (2008)

Advances in Difference Equations [electronic only]

On the difference property of families of measurable functions

Rafał Filipów (2003)

Colloquium Mathematicae

We show that, generally, families of measurable functions do not have the difference property under some assumption. We also show that there are natural classes of functions which do not have the difference property in ZFC. This extends the result of Erdős concerning the family of Lebesgue measurable functions.

On the differentiability of solutions of a functional equation with respect to a parameter

S. Czerwik (1971)

Annales Polonici Mathematici

On the discrete maximum principle for parabolic difference operators

Hung-Ju Kuo, N. S. Trudinger (1993)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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