The solution of the functional equation of d'Alembert's type for commutative groups.
The spectral matrices of Toda solitons and the fundamental solution of some discrete heat equations
The Stieltjes spectral matrix measure of the doubly infinite Jacobi matrix associated with a Toda -soliton is computed, using Sato theory. The result is used to give an explicit expansion of the fundamental solution of some discrete heat equations, in a series of Jackson’s -Bessel functions. For Askey-Wilson type solitons, this expansion reduces to a finite sum.
The stability analysis of a discretized pantograph equation
The paper deals with a difference equation arising from the scalar pantograph equation via the backward Euler discretization. A case when the solution tends to zero but after reaching a certain index it loses this tendency is discussed. We analyse this problem and estimate the value of such an index. Furthermore, we show that the utilized proof technique enables us to investigate some other numerical formulae, too.
The stability cone for a matrix delay difference equation.
The stability of a quadratic functional equation with the fixed point alternative.
The stability of Markov operators on Polish spaces
A sufficient condition for the asymptotic stability of Markov operators acting on measures defined on Polish spaces is presented.
The stability of multiplicative semigroup homomorphisms to real normed algebras, I.
The stability of some linear functional equations.
The stability of the equation on groups.
The structure of disjoint iteration groups on the circle
The aim of the paper is to investigate the structure of disjoint iteration groups on the unit circle , that is, families of homeomorphisms such that and each either is the identity mapping or has no fixed point ( is an arbitrary -divisible nontrivial (i.e., ) abelian group).
The structure of iteration groups of continuous functions.
The structure of iteration groups of continuous functions. (Summary).
The superstability of the generalized d'Alembert functional equation.
The translation equation and algebraic objects
The translation equation on a direct product of groups
The translation equation on certain n-groups.
The Ulam stability problem in approximation of approximately quadratic mappings by quadratic mappings.
The Uniqueness of Solutions of a System of Functional Equations in Some Classes of Functions.
The zero distribution and uniqueness of difference-differential polynomials
We consider the zero distribution of difference-differential polynomials of meromorphic functions and present some results which can be seen as the discrete analogues of the Hayman conjecture. In addition, we also investigate the uniqueness of difference-differential polynomials of entire functions sharing one common value. Our theorems improve some results of Luo and Lin [J. Math. Anal. Appl. 377 (2011), 441-449] and Liu, Liu and Cao [Appl. Math. J. Chinese Univ. 27 (2012), 94-104].
Theorems of Thron's type for random-valued vector functions and the Krein-Rutman theorem
We propose stochastic versions of some theorems of W. J. Thron [14] on the speed of convergence of iterates for random-valued functions on cones in Banach spaces.