The global attractivity of difference equations of nonincreasing nonlinearities with applications

Convergence to equilibria in discrete population models

“…Our main result in this paper extends Theorem 3.1 in ref. [2] and, in particular, improves Theorem 1.2 when f satisfies (H). As a result, we find sharper conditions for the convergence of all positive solutions of equations (1.3) and (1.4) to the corresponding equilibria.…”

“…[2] a new global stability result was proved which applies in some cases for which equation (1.10) does not hold. However, both results are not comparable.…”

On the Global Stability of One Nonlinear Difference Equation

“…The purpose of the present paper is the investigation of the global stability of the unique fixed point of Eq. (1). The global stability of various partial classes of Eqs.…”

“…The global stability of various partial classes of Eqs. (1) was studied in [1][2][3][4][5][6][7][8][9][10][11]. We define a functional M : R k+1 → R + as follows: M(φ) = max i {0, φ i }.…”

“…(1). For every k, condition (5) is exact for the subclass of equations (1) satisfying conditions H and the restriction b = 0, q ∈ (0, q k ].…”