Stevo Stević

On an integral operator on the unit ball in

Let denote the space of all holomorphic functions on the unit ball. In this paper, we investigate the integral operator,,, where and is the radial derivative of. The operator can be considered as an extension of the Cesàro operator on the unit disk. The boundedness of the operator on-Bloch spaces is considered.

Existence of nontrivial solutions of a rational difference equation

Abstract We prove that the Putnam difference equation x n + 1 = x n + x n − 1 + x n − 2 x n − 3 x n x n − 1 + x n − 2 + x n − 3 , n = 0 , 1 , … has a positive solution which is not eventually equal to 1. This provides positive confirmation of a conjecture due to G. Ladas [Open problems and conjectures, J. Difference Equ. Appl. 4 (1998) 497–499].

On positive solutions of a (k+1)th order difference equation

Abstract In this work we show that the following difference equation: x n + 1 = x n − k 1 + x n + ⋯ + x n − k + 1 , n = 0 , 1 , … , where k ∈ N is fixed, has a positive solution which converges to zero. This result solves Open Problem 11.4.10 (a) in [M.R.S. Kulenovic, G. Ladas, Dynamics of Second Order Rational Difference Equations. With Open Problems and Conjectures, Chapman and Hall/CRC, 2001].

On the recursive sequence xn+1=max{c,xnpxn−1p}

Abstract This work studies the boundedness and global attractivity for the positive solutions of the difference equation x n + 1 = max { c , x n p x n − 1 p } , n ∈ N 0 , with p , c ∈ ( 0 , ∞ ) . It is shown that: (a) there exist unbounded solutions whenever p ≥ 4 , (b) all positive solutions are bounded when p ∈ ( 0 , 4 ) , (c) every positive solution is eventually equal to 1 when p ∈ ( 0 , 4 ) and c ≥ 1 , (d) all positive solutions converge to 1 whenever p , c ∈ ( 0 , 1 ) .

On a system of difference equations

Abstract We show that the system of difference equations x n + 1 = ax n - 1 by n x n - 1 + c , y n + 1 = α y n - 1 β x n y n - 1 + γ , n ∈ N 0 , where the parameters a , b , c , α , β , γ and initial values x −1 , x 0 , y −1 , y 0 are real numbers, can be solved, considerably improving the results in the literature.

A short proof of the Cushing-Henson conjecture

We give a short proof of the Cushing-Henson conjecture concerning Beverton-Holt difference equation, which is important in theoretical ecology. The main result shows that a periodic environment is always deleterious for populations modeled by the Beverton-Holt difference equation.

ON AN INTEGRAL OPERATOR FROM THE ZYGMUND SPACE TO THE BLOCH-TYPE SPACE ON THE UNIT BALL

In this paper, we introduce an integral operator on the unit ball . The boundedness and compactness of the operator from the Zygmund space to the Bloch-type space or the little Bloch-type space are investigated.

Products of composition and integral type operators from H ∞ to the Bloch space

We study the boundedness and compactness of the products of composition operators and integral type operators from H ∞ to the Bloch space on the unit disk.

Weighted Composition Operators from H∞ to the Bloch Space on the Polydisc

Let Dn be the unit polydisc of ℂn, ϕ(z)=(ϕ1(z),…,ϕn(z)) be a holomorphic self-map of Dn, and ψ(z) a holomorphic function on Dn. Let H(Dn) denote the space of all holomorphic functions with domain Dn, H∞(Dn) the space of all bounded holomorphic functions on Dn, and B(Dn) the Bloch space, that is, B(Dn)={f∈H(Dn)|‖f‖B=|f(0)|

Norm and essential norm of composition followed by differentiation from α-Bloch spaces to Hμ∞

Abstract This note calculates the norm of composition followed by differentiation operator from the Bloch and the little Bloch space to the weighted space H μ ∞ on the unit disk, and gives an upper and a lower bound for the essential norm of the operator from the α -Bloch space B α , α > 0 to H μ ∞ .