In this paper the difference equation

Δxn=unφ(xσ (n))

is considered. For a given b ∈ ℝ, and assuming the absolute convergence of the series ∑ un, we investigate the properties of a function φ sufficient for the existence of a solution convergent to b. It is known that the continuity of φ on some neighborhood of b is sufficient for the existence of such solution. The main result of this paper is the example in which we show that the continuity at the point b is not sufficient.

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