Recently, there has been a lot of interest in studying the global attractivity, the boundedness character, and the periodicity nature of nonlinear difference equations see for example, [1– 22]. The study of the nonlinear rational difference equations of a higher order is quite challenging and rewarding, and the results about these equations offer prototypes towards the development of the basic ...

We study the global stability, the periodic character, and the boundedness character of the positive solutions of the difference equation xn 1 α − βxn / γ − δxn − xn−k , n 0, 1, 2, . . . , k ∈ {1, 2, . . .}, in the two cases: i δ ≥ 0, α > 0, γ > β > 0; ii δ ≥ 0, α 0, γ, β > 0, where the coefficients α, β, γ, and δ, and the initial conditions x−k, x−k 1, . . . , x−1, x0 are real numbers. We show...

In this paper we study the asymptotic behavior of the solution of the new class of the nonlinear rational Difference Equations. Namely, we consider the stability, boundedness, and periodicity of the solution. Moreover we give the periodic character of solutions of these equations, which is not familiar. We do not know a similar feature for other class of the nonlinear rational Difference Equati...

Recently there has been a lot of interest in studying the global attractivity, the boundedness character, and the periodicity nature of nonlinear difference equations. In [5, 6, 8] some global convergence results were established which can be applied to nonlinear difference equations in proving that every solution of these equations converges to a periodic solution (which need not necessarily b...

a new definition of boundedness of linear order-homomorphisms (loh)in $l$-topological vector spaces is proposed. the new definition iscompared with the previous one given by fang [the continuity offuzzy linear order-homomorphism, j. fuzzy math. 5 (4) (1997)829$-$838]. in addition, the relationship between boundedness andcontinuity of lohs is discussed. finally, a new uniform boundednessprincipl...

Recently, Brannan and Vergnioux showed that the free orthogonal quantum group factors $\mathcal{L}\mathbb{F}O_M$ have Jung's strong 1-boundedness property, hence are not isomorphic to factors. We prove an analogous result for other unimodular case, where parameter matrix is standard symplectic in 2N dimensions $J_{2N}$. compute derivatives of defining relations by introducing self-adjoint gener...

in the present paper, we rst modify the concepts of weakly fuzzy boundedness, strongly fuzzy boundedness, fuzzy continuity, strongly fuzzy continuity and weakly fuzzy continuity. then, we try to nd some relations by making a comparative study of the fuzzy norms of linear operators.

A new definition of boundedness of linear order-homomorphisms (LOH)in $L$-topological vector spaces is proposed. The new definition iscompared with the previous one given by Fang [The continuity offuzzy linear order-homomorphism, J. Fuzzy Math. 5 (4) (1997)829$-$838]. In addition, the relationship between boundedness andcontinuity of LOHs is discussed. Finally, a new uniform boundednessprincipl...

Recently, there has been a great interest in studying the behavior of rational and nonlinear difference equations; see, for example, [1–20]. One of the most intriguing properties of solutions of difference equations is their boundedness character. There are numerous papers devoted, among others, to this research area, see; for example, [1–6, 9–19], and related references therein. It is said tha...