Global attractivity for a nonlinear difference equation with variable delay

In this paper, we give sufficient conditions under which every solution of the nonlinear difference equation with variable delay x(n + 1) − x(n) + pnf(x(g(n))) = 0, n = 0, 1, 2, … tends to zero as n → ∞. Here, pn is a nonnegative sequence, f : R → R is a continuous function with xf(x) > 0 if x ≠ 0, and g : N → Z is nondecreasing and satisfies g(n) ≤ n for n ≥ 0 and limn→∞ g(n) = ∞.