Showing papers by "Stevo Stević published in 2021"

On a class of difference equations with interlacing indices

Abstract: Some results on the long-term behavior of solutions to a class of difference equations, which includes numerous nonlinear difference equations of various orders that attracted some attention in the last 15 years, are presented. We also present a natural connection among these difference equations, compare some results on the equations with some other ones in the literature, and give a list of a considerable number of difference equations which can be treated in a similar way.

On a class of solvable difference equations generalizing an iteration process for calculating reciprocals

Abstract: The well-known first-order nonlinear difference equation $$ y_{n+1}=2y_{n}-xy_{n}^{2}, \quad n\in {\mathbb {N}}_{0}, $$ naturally appeared in the problem of computing the reciprocal value of a given nonzero real number x. One of the interesting features of the difference equation is that it is solvable in closed form. We show that there is a class of theoretically solvable higher-order nonlinear difference equations that include the equation. We also show that some of these equations are also practically solvable.

Note on norm of an m -linear integral-type operator between weighted-type spaces

Abstract: We find a necessary and sufficient condition for the boundedness of an m-linear integral-type operator between weighted-type spaces of functions, and calculate norm of the operator, complementing some results by L. Grafakos and his collaborators. We also present an inequality which explains a detail in the proof of the boundedness of the linear integral-type operator on $L^{p}({\mathbb {R}}^{n})$ space.

Note on theoretical and practical solvability of a class of discrete equations generalizing the hyperbolic-cotangent class

Abstract: There has been some recent interest in investigating the hyperbolic-cotangent types of difference equations and systems of difference equations. Among other things their solvability has been studied. We show that there is a class of theoretically solvable difference equations generalizing the hyperbolic-cotangent one. Our analysis shows a bit unexpected fact, namely that the solvability of the class is based on some algebraic relations, not closely related to some trigonometric ones, which enable us to solve them in an elegant way. Some examples of the difference equations belonging to the class which are practically solvable are presented, as well as some interesting comments on connections of the equations with some iteration processes.

Note on constructing a family of solvable sine-type difference equations

Abstract: We obtain a family of first order sine-type difference equations solvable in closed form in a constructive way, and we present a general solution to each of the equations

Note on a discrete initial value problem from a competition

Abstract: The following discrete initial value problem $$ x_{n+1}=x_{n}\bigl(x_{n-1}^{2}-2 \bigr)-x_{1},\quad n\in {\mathbb{N}}, $$ $x_{0}=2$ and $x_{1}=5/2$ , appeared at an international competition It is known that the problem can be solved in closed form Here we discuss the solvability of a more general initial value problem which includes the former one We show that, in a sense, there are not so many solvable discrete initial value problems related to this one, showing its specificity, which is a bit surprising result