On the recursive sequence χn+1 = χn-1/g(χn)

Abstract

In [5] the following problem was posed. Is there a solution of the following difference equation χn+1 = n βχn-1/β + χn, χ-1,χ0 > 0, β > 0, n = 0, 1, 2, ... such that χn → 0 as n → ∞. We prove a result which, as a special case, solves the above problem.