Showing papers by "Stevo Stević published in 2022"
TL;DR: In this article , Moaaz et al. presented an example of a difference equation of arbitrary order, possessing the right-hand side function that is homogeneous to a certain degree and nonincreasing in each variable, which has a unique positive equilibrium, as well as solutions that do not converge to the equilibrium.
Abstract: Abstract We present an example of a difference equation of arbitrary order, possessing the right-hand side function that is homogeneous to a certain degree and nonincreasing in each variable, which has a unique positive equilibrium, as well as solutions that do not converge to the equilibrium. The example shows that the main result in the paper: O. Moaaz, Dynamics of difference equation $x_{n+1}=f(x_{n-l}, x_{n-k})$ x n + 1 = f ( x n − l , x n − k ) (Adv. Differ. Equ. 2018:447, 2018), is incorrect.
5 citations
TL;DR: In this paper , a nonlinear second-order difference equation was studied and it was shown that the difference equation is solvable in closed form, and some applications of the main result were also given.
Abstract: Abstract We study a nonlinear second-order difference equation which considerably extends some equations in the literature. Our main result shows that the difference equation is solvable in closed form. Some applications of the main result are also given.
5 citations
TL;DR: In this paper , Moaaz et al. presented an example of a difference equation of arbitrary order, possessing the right-hand side function that is homogeneous to a certain degree and nonincreasing in each variable, which has a unique positive equilibrium, as well as solutions that do not converge to the equilibrium.
Abstract: Abstract We present an example of a difference equation of arbitrary order, possessing the right-hand side function that is homogeneous to a certain degree and nonincreasing in each variable, which has a unique positive equilibrium, as well as solutions that do not converge to the equilibrium. The example shows that the main result in the paper: O. Moaaz, Dynamics of difference equation $x_{n+1}=f(x_{n-l}, x_{n-k})$ x n + 1 = f ( x n − l , x n − k ) (Adv. Differ. Equ. 2018:447, 2018), is incorrect.
5 citations
TL;DR: In this paper , the boundedness and compactness of the operator Su→,φm=∑j=0mMujCφℜj$$ {\mathfrak{S}}_{\overrightarrow{u,\varphi}^m={\sum}_{j= 0}^n{M}_{u_j}{C}_{\varpi }{\Re}^j
Abstract: We investigate the boundedness and compactness of the operator Su→,φm=∑j=0mMujCφℜj$$ {\mathfrak{S}}_{\overrightarrow{u},\varphi}^m={\sum}_{j=0}^m{M}_{u_j}{C}_{\varphi }{\Re}^j $$ , where Muj$$ {M}_{u_j} $$ is the multiplication operator with symbol uj,j∈{0,1,⋯,m}$$ {u}_j,j\in \left\{0,1,\cdots, m\right\} $$ , which are holomorphic functions on the open unit ball 𝔹 in ℂn,Cφ$$ {\mathbb{C}}^n,{C}_{\varphi } $$ the composition operator with symbol φ$$ \varphi $$ which is a holomorphic self‐map of 𝔹 , and ℜj$$ {\Re}^j $$ the j$$ j $$ th iterated radial derivative operator, from the Hardy space Hp$$ {H}^p $$ to the weighted‐type space Hμ∞$$ {H}_{\mu}^{\infty } $$ on 𝔹 .
4 citations
TL;DR: In this paper , a nonlinear second-order difference equation was studied and it was shown that the difference equation is solvable in closed form, and some applications of the main result were also given.
Abstract: Abstract We study a nonlinear second-order difference equation which considerably extends some equations in the literature. Our main result shows that the difference equation is solvable in closed form. Some applications of the main result are also given.
3 citations
TL;DR: In this article , the integral norm and essential norm of an integral type operator from the logarithmic Bloch space and the little log-a-bloch space to Bloch-type spaces on the unit ball were calculated.
Abstract: We calculate norm and essential norm of an integral‐type operator from the logarithmic Bloch space and the little logarithmic Bloch space to Bloch‐type spaces on the unit ball of ℂn$$ {\mathbb{C}}^n $$ . We show that there is a one‐parameter class of equivalent norms on the logarithmic Bloch space for which the norms can be calculated.
2 citations
TL;DR: In this paper , a class of nonlinear difference equations of the fourth order is considered and it is shown that the class of equations is solvable in closed form explaining theoretically, among other things, solvability of some previously considered very special cases.
Abstract: We consider a class of nonlinear difference equations of the fourth order, which extends some equations in the literature. It is shown that the class of equations is solvable in closed form explaining theoretically, among other things, solvability of some previously considered very special cases. We also present some applications of the main theorem through two examples, which show that some results in the literature are not correct.
1 citations
1 citations
TL;DR: The boundedness and compactness of linear operators from the weighted Bergman space to the weighted type spaces on the unit ball were characterized in this article , where a new class of linear operator was introduced.
Abstract:
The boundedness and compactness of a new class of linear operators from the weighted Bergman space to the weighted-type spaces on the unit ball are characterized.
TL;DR: In this article , the authors present thirty-six classes of three-dimensional systems of difference equations of the hyperbolic-cotangent type which are solvable in closed form.
Abstract: We present thirty-six classes of three-dimensional systems of difference equations of the hyperbolic-cotangent type which are solvable in closed form.
TL;DR: In this article , a comparison method and some difference inequalities were used to show that the following higher order difference equation $$ x n+k =\frac{1}{f(xn+k-1},\ldots ,x_{n})},\quad n\in{\mathbb{N}},$$
Abstract: Abstract By using a comparison method and some difference inequalities we show that the following higher order difference equation $$ x_{n+k}=\frac{1}{f(x_{n+k-1},\ldots ,x_{n})},\quad n\in{\mathbb{N}},$$ x n + k = 1 f ( x n + k − 1 , … , x n ) , n ∈ N , where $k\in{\mathbb{N}}$ k ∈ N , $f:[0,+\infty )^{k}\to [0,+\infty )$ f : [ 0 , + ∞ ) k → [ 0 , + ∞ ) is a homogeneous function of order strictly bigger than one, which is nondecreasing in each variable and satisfies some additional conditions, has unbounded solutions, presenting a large class of such equations. The class can be used as a useful counterexample in dealing with the boundedness character of solutions to some difference equations. Some analyses related to such equations and a global convergence result are also given.
TL;DR: In this article, the norms of several concrete operators, mostly of some integral-type ones between weighted-type spaces of continuous functions on several domains, are calculated, and the norm of an integral type operator on some subspaces of the weighted Lebesgue spaces.
Abstract: We calculate the norms of several concrete operators, mostly of some integral-type ones between weighted-type spaces of continuous functions on several domains. We also calculate the norm of an integral-type operator on some subspaces of the weighted Lebesgue spaces.
TL;DR: In this article , a comparison method and some difference inequalities were used to show that the following higher order difference equation $$ x n+k =\frac{1}{f(xn+k-1},\ldots ,x_{n})},\quad n\in{\mathbb{N}},$$
Abstract: Abstract By using a comparison method and some difference inequalities we show that the following higher order difference equation $$ x_{n+k}=\frac{1}{f(x_{n+k-1},\ldots ,x_{n})},\quad n\in{\mathbb{N}},$$ x n + k = 1 f ( x n + k − 1 , … , x n ) , n ∈ N , where $k\in{\mathbb{N}}$ k ∈ N , $f:[0,+\infty )^{k}\to [0,+\infty )$ f : [ 0 , + ∞ ) k → [ 0 , + ∞ ) is a homogeneous function of order strictly bigger than one, which is nondecreasing in each variable and satisfies some additional conditions, has unbounded solutions, presenting a large class of such equations. The class can be used as a useful counterexample in dealing with the boundedness character of solutions to some difference equations. Some analyses related to such equations and a global convergence result are also given.
TL;DR: In this paper , the integer parts of the reciprocal remainders of the zeta function were generalized to linear difference equations with constant coefficients, and a very short and elegant proof was given.
Abstract: Abstract We present generalizations of some results on the integer parts of the reciprocal remainders of the zeta function $\zeta (s)$ ζ ( s ) with $s=2$ s = 2 and $s=3$ s = 3 , and a very short and elegant proof of a recent result on the integer parts of the reciprocal remainders of the series $\zeta (3)$ ζ ( 3 ) . We also give some historical and theoretical remarks to problems of this type, conduct some analyses, and make some connections with the theory of linear difference equations with constant coefficients.