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We investigate the periodic character of solutions of the nonlinear difference equation xn

We present a closed-form formula for the general solution to the difference equation x n + k − q n x n = f n , n ∈ N 0 , $$x_{n+k}-q_{n}x_{n}=f_{n},\quad n\in \mathbb {N}_{0}, $$ where k ∈ N $k\in \mathbb {N}$ , ( q n ) n ∈ N 0 $(q_{n})_{n\in \mathbb {N}_{0}}$ , ( f n ) n ∈ N 0 ⊂ C $(f_{n})_{n\in \mathbb {N}_{0}}\subset \mathbb {C}$ , in the case q n = q $q_{n}=q$ , n ∈ N 0 $n\in...

We present a closed-form formula for the general solution to the difference equation x n + k − q n x n = f n , n ∈ N 0 , $$x_{n+k}-q_{n}x_{n}=f_{n},\quad n\in \mathbb {N}_{0}, $$ where k ∈ N $k\in \mathbb {N}$ , ( q n ) n ∈ N 0 $(q_{n})_{n\in \mathbb {N}_{0}}$ , ( f n ) n ∈ N 0 ⊂ C $(f_{n})_{n\in \mathbb {N}_{0}}\subset \mathbb {C}$ , in the case q n = q $q_{n}=q$ , n ∈ N 0 $n\in...

We present a closed-form formula for the general solution to the difference equation x n + k − q n x n = f n , n ∈ N 0 , $$x_{n+k}-q_{n}x_{n}=f_{n},\quad n\in \mathbb {N}_{0}, $$ where k ∈ N $k\in \mathbb {N}$ , ( q n ) n ∈ N 0 $(q_{n})_{n\in \mathbb {N}_{0}}$ , ( f n ) n ∈ N 0 ⊂ C $(f_{n})_{n\in \mathbb {N}_{0}}\subset \mathbb {C}$ , in the case q n = q $q_{n}=q$ , n ∈ N 0 $n\in...

A solvable class of product-type systems of difference equations with two dependent variables on the complex domain is presented. The main results complement some recent ones in the literature, while their proofs contain some refined methodological details. We provide closed form formulas for general solutions to the system or give procedures for how to get them. MSC: 39A20, 39A45.

By modifying our recent method of half-lines we show how the following boundary value problem for partial difference equations can be solved in closed form: d n , k = d n − 1 , k − 1 + f ( k ) d n − 1 , k , 1 ≤ k < n , d n , 0 = u n , d n , n = v n , n ∈ N , where ( u n ) n ∈ N and ( v n ) n ∈ N are given sequences of complex numbers, and f is a complex-valued function on N . MSC...

Some sufficient conditions are given such that the following system of difference equations: x ( 1 ) ( n + 1 ) = max 1 ≤ j ≤ l 1 { f 1 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , x ( 2 ) ( n + 1 ) = max 1 ≤ j ≤ l 2 { f 2 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , ⋮ x ( k ) ( n + 1 ) = max 1 ≤ j ≤ l k { f k j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , n ∈ N 0 , where k...

A solvable two-dimensional product-type system of difference equations of interest is presented. Closed form formulas for its general solution are given. MSC: 39A10, 39A20.

We characterize the boundedness and compactness of a product-type operator, which, among others, includes all the products of the single composition, multiplication, and differentiation operators, from a general space to Bloch-type spaces. We also give some upper and lower bounds for the norm of the operator. MSC: 47B38, 46E15.

Some criteria for the boundedness, as well as for the compactness, of the generalized weighted composition operator D φ , u n from α-Bloch spaces into weighted-type spaces are given. Estimates for the norm and the essential norm of the operator are also given. Our results extend and complement some results in the literature. MSC: 47B33, 30H30.

Let σ be a Békollé weight function and ν be a weight function. In this paper, we characterize the boundedness and compactness of weighted composition operators acting from Bergman-type spaces A p ( σ ) to Bloch-type spaces B ν and B ν , 0 , considerably extending some results in the literature. MSC: 47B33, 46E10, 30D55.

The boundedness character of positive solutions of the following system of difference equations: x n + 1 = A + y n p x n − 3 r , y n + 1 = A + x n p y n − 3 r , n ∈ N 0 , when min { A , r } > 0 and p ≥ 0 , is studied. MSC: 39A10, 39A20.

It is shown that the following system of difference equations z n + 1 = z n a w n − 1 b , w n + 1 = w n c z n − 1 d , n ∈ N 0 , where a , b , c , d ∈ Z , z − 1 , z 0 , w − 1 , w 0 ∈ C , is solvable in closed form. MSC: 39A10, 39A20.

Closed form formulas of the solutions to the following system of difference equations: x n = y n − 1 y n − 2 x n − 1 ( a n + b n y n − 1 y n − 2 ) , y n = x n − 1 x n − 2 y n − 1 ( α n + β n x n − 1 x n − 2 ) , n ∈ N 0 , where a n , b n , α n , β n , n ∈ N 0 , and initial values x − i , y − i , i ∈ { 1 , 2 } are real numbers, are found. The domain of undefinable solutions to the...

We obtain some new characterizations for the Bloch space on the open unit disk in the complex plane ℂ and the open unit ball of Cn.MSC: 32A18.

: Josef Diblik
Copyright © 2014 **Stevo** **Stević** et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and

, P.O. Box 42641, Jeddah 21551, Saudi Arabia
Received 25 September 2013; Accepted 22 October 2013
Academic Editor: Josef Diblík
Copyright © 2013 **Stevo** **Stević** et al. This is an open access article

, P.O. Box 42641, Jeddah 21551, Saudi Arabia
Received 25 September 2013; Accepted 22 October 2013
Academic Editor: Josef Diblík
Copyright © 2013 **Stevo** **Stević** et al. This is an open access article