GLOBAL ATTRACTIVITY IN A FOUR-TERM RECURRENCE RELATION

Abstract

where (Hl) f: (O,oo) -t Rand g: [O,oo) x [O,oo) -t Rare positive functions; and (H2) f is nondecreasing and g is nonincreasing in each of its independent variables. A positive fixed point x* that satisfies x = f(x)g(x, x) is also called a positive equi­ librium point of equation (1.1). Our objective of this note is to show that under mild conditions on the functions f and g, every real sequence in n tends to one of the positive equilibrium points of (1.1). Similar results have been obtained for a number of recureence relations, see e.g. Kocic and Ladas [1], Camouzis et al. [2], Li et al. [3], and Li [4]. Indeed, this note is motivated by a concern raised in Kocic and Ladas [1, p.46] related to the stability of recurrence relations.