This paper studies global asymptotic stability for positive solutions to the equation yn = yn−k + yn−m 1 + yn−k yn−m , n = 0, 1, . . . , with y−m , y−m+1, . . . , y−1 ∈ (0,∞) and 1 ≤ k < m. The paper includes a discussion of stability for a wide class of symmetric rational difference equations which includes the type studied here as well as several other in the recent literature. c © 2006 Elsev...

Abstract Discrete systems are often described by difference equations. With some attributes of initial state type, a difference equation defines a system, i.e. a set of (input,output) pairs. For systems defined by linear difference equations (with constant or variable coefficients) on arbitrary sets A ⊂ Z sufficient conditions of their stability are formulated. It is also shown that these condi...

the starting point of this paper is given by priestley’s papers, where a theory of representation of distributive lattices is presented. the purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. in this way, some results of priestley’s papers are extended. in the main theorem, we show that the category of finite fuzzy priestley space...

in this paper, we study the finitely many constraints of the fuzzyrelation inequality problem and optimize the linear objectivefunction on the region defined by the fuzzy max-product operator.simplification operations have been given to accelerate theresolution of the problem by removing the components having noeffect on the solution process. also, an algorithm and somenumerical and applied exa...

In this note, we consider the following rational difference equation: xn+1 = f (xn−r1 , . . . , xn−rk )g(xn−m1 , . . . , xn−ml )+ 1 f (xn−r1 , . . . , xn−rk )+ g(xn−m1 , . . . , xn−ml ) , n= 0,1, . . . , where f ∈ C((0,+∞)k, (0,+∞)) and g ∈ C((0,+∞)l, (0,+∞)) with k, l ∈ {1,2, . . .}, 0 r1 < · · ·< rk and 0 m1 < · · ·<ml , and the initial values are positive real numbers. We give sufficient con...

We study a scalar linear difference equation with several delays by transforming it to a system of Volterra equations without delays. The results obtained for this system are then used to establish oscillation criteria and asymptotic properties of solutions of the considered equation.

It is well known fact that binary relations are generalized mathematical functions. Contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. Some basic operations on functions such as the inverse and composition are applicable to binary relations as well. Depending on the domain or range or both are fuzzy value fuzzy set, i...

We give a complete picture regarding the behavior of positive solutions of the following important difference equation: xn = 1+ ∑ k i=1αixn−pi / ∑m j=1βjxn−qj , n∈N0, where αi, i∈ {1, . . . ,k}, and βj , j ∈ {1, . . . ,m}, are positive numbers such that ∑ k i=1αi = ∑m j=1βj = 1, and pi, i ∈ {1, . . . ,k}, and qj , j ∈ {1, . . . ,m}, are natural numbers such that p1 < p2 < ··· < pk and q1 < q2 <...