* Correspondence: [email protected] Department of Basic Courses, Hebei Finance University, Baoding 071000, China Abstract This article is concerned with the following rational difference equation yn+1 = (yn + yn-1)/(p + ynyn-1) with the initial conditions; y-1, y0 are arbitrary positive real numbers, and p is positive constant. Locally asymptotical stability and global attractivity of the ...

The author continues to study series transformations for the Euler-Mascheroni constant γ . Here, we discuss in detail recently published results of A. I. Aptekarev and T. Rivoal who found rational approximations to γ and γ log q q ∈ Q>0 defined by linear recurrence formulae. The main purpose of this paper is to adapt the concept of linear series transformations with integral coefficients such t...

We prove a comparison theorem for the solutions of a rational matrix difference equation, generalizing the Riccati difference equation, and existence and convergence results for the solutions of this equation. Moreover we present conditions ensuring that the corresponding algebraic matrix equation has a stabilizing or almost stabilizing solution. AMS Classification: 39A10, 93E03.

This paper looks at the approach of using generating functions to solve linear inhomogeneous recurrence equations with constant coefficients. It will be shown that the generating functions for these recurrence equations are rational functions. By decomposing a generating function into partial fractions, one can derive explicit formula as well as asymptotic estimates for its coefficients. Key–Wo...

lie in finitely many proper subspaces of Q. As an application of the subspace theorem Schmidt [16] described all norm form equations that have finitely many solutions. The subspace theorem has been further developed by Schlickewei [11, 12] and is proved in it’s most general form by Evertse and Schlickewei [3] (see also [13]). These investigations led to many applications, e.g. to the finiteness...

Dedicated to Prof. Jaroslav Kurzweil on the occasion of his 80th birthday Abstract. Asymptotic properties of the half-linear difference equation (∗) ∆(an|∆xn| α sgn∆xn) = bn|xn+1| α sgnxn+1 are investigated by means of some summation criteria. Recessive solutions and the Riccati difference equation associated to (∗) are considered too. Our approach is based on a classification of solutions of (...

Recessive and dominant solutions for the nonoscillatory half-linear difference equation are investigated. By using a uniqueness result for the zero-convergent solutions satisfying a suitable final condition, we prove that recessive solutions are the “smallest solutions in a neighborhood of infinity,” like in the linear case. Other asymptotic properties of recessive and dominant solutions are tr...

Abstract. Mean field type models describing the limiting behavior of stochastic differential games as the number of players tends to +∞, have been recently introduced by J-M. Lasry and P-L. Lions. Under suitable assumptions, they lead to a system of two coupled partial differential equations, a forward Bellman equation and a backward Fokker-Planck equations. Finite difference schemes for the ap...

The aim of this paper is to prove that given a linear recurrence sequence U = kb u„ +z = u„ + , + u„, n w 1, u t =1, uz > u l , then the set of positive integers can be partitioned uniquely into two disjoint subsets such that the sum of any two distinct members from any one set can never be in U and study related problems . We prove our main result in Section 2. In Section 3 we give a graph the...

We consider log-convex sequences that satisfy an additional constraint imposed on their rate of growth. We call such sequences log-balanced. It is shown that all such sequences satisfy a pair of double inequalities. Sufficient conditions for log-balancedness are given for the case when the sequence satisfies a two(or more-) term linear recurrence. It is shown that many combinatorially interesti...