Results 231 to 240 of about 151,638 (261)

Iteration Theory: Dynamical Systems and Functional Equations

International Journal of Bifurcation and Chaos, 2003
The aim of this paper is to give an account of some problems considered in the past years in the setting of Discrete Dynamical Systems and Iterative Functional Equations, some new research directions and also state some open problems.
Francisco Balibrea, Ludwig Reich, Jaroslav Smítal   +2 more
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Systems of functional equations and generalizations of certain functions

Aequationes mathematicae, 2021
In this article generalized Salem functions and a generalized shift operator are studied. The author studies a particular generalization of the shift operator which gives a series that generalizes the \(q\)-ary expansion of a number and models numeral systems with a variable alphabet.
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Analytic solutions of systems of functional equations

Applied Mathematics-A Journal of Chinese Universities, 2003
For a function \(f\) denote by \(f^n\) its \(n\)-th iterate. For a function \(H\) of \(n\) variables put \(\Psi _H (f)(z)=H(z,f(z), f^2(z),\dots,f^{n-1}(z)).\) The author studies a system of functional equations involving two functions \(f\) and \(g\) as well as the functions \(\Psi_{H_j}(f)\) and \(\Psi_{K_j}(g)\) with certain functions \(H_j\) and ...
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Near-equational and equational systems of logic for partial functions. II

The Journal of Symbolic Logic, 1989
For the reader's convenience, we begin Part II by restating the rules for constructing Sq derivations given in §2: We let R be the set of 14 rules for Sq, R * the set of ...
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On the Asymptotic Behaviour of the Solutions of a System of Functional Equations

Periodica Mathematica Hungarica, 2000
Motivated by some results on the pantograph-type differential equation \[ x'(t)=A(t)x(t)+B(t)x(\lambda t), \] the asymptotic behaviour of the solutions of the functional equation \[ x(t)=A(t)x(t-1)+B(t)x(p(t)) \] is investigated.
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On a System of Functional Equations in a Multi-Dimensional Domain

Zeitschrift für Analysis und ihre Anwendungen, 2000
We study the system of functional equations f_i(x) = \sum^n_{j=1} \sum^m_{k=1} a_{ijk} [x, f_i (S_{ijk} (x))] + g_i (x) \ \ (l ≤ i ≤n) for x \in \Omega_i
Long, N. T., Nghia, N. H.
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Constructive Solutions for Systems of Iterative Functional Equations

Constructive Approximation, 2016
This comprehensive paper studies the systems of iterative functional equations. Generally, they are of the following form. Let \(X,Y\) be nonempty sets and \(p\geq2\) an integer. For \(X_i\subset X\), \(\bigcup_{i=0}^{p-1}X_i=X\), \(W_i\subset X\) and given functions \(f_i: X_i\to W_i\) and \(F_i: X_i\times Y\to Y\) (\(i=0,1,\dots,p-1\)) we consider ...
Serpa, Cristina, Buescu, Jorge
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Solution of two systems of functional equations

Matematicheskie Trudy
In this article, we solve two systems of functional equations that arise as a result of solving the problem of embedding an additive and multiplicative two-dimensional phenomenologically symmetric geometry of rank (2,2) into one of the two-dimensional phenomenologically symmetric geometries of rank (3,2).
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Periodic Solutions of the Systems of Nonlinear Functional Equations

Journal of Mathematical Sciences, 2014
The authors study the following system of nonlinear functional equations of the form \[ x(t) = F(t, x(q_1 t + f_1 (t, x(t))), \dots, x(q_k t + f_k (t, x(t)))), \tag{1} \] where \(F: \mathbb{R} \times \mathbb{R}^n \times \cdots \times \mathbb{R}^n \to \mathbb{R}^n\), \(f_i : \mathbb{R} \times \mathbb{R}^n \to \mathbb{R}\), and \(q_i\)'s are positive ...
Pelyukh, H. P., Syvak, O. A.
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On Analytic Iterative Functions for Solving Nonlinear Equations and Systems of Equations

2005
Let ϕ be analytic iterative vector function with fixed point α and integer order p > 1. It is proved that for each approximation z0 of α and enough close to α the corresponding iterative process zk+1=ϕ(zk) converges to α with order p. Using this result we give new shorter proofs for convergence of some well known iterative methods and of iterative ...
Gyurhan Nedzhibov, Milko G. Petkov
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