Abstract
Let [Formula: see text] be a triangular algebra over a commutative ring [Formula: see text]. In this paper, under some mild conditions on [Formula: see text], we prove that if [Formula: see text] is a nonlinear map satisfying [Formula: see text] for any [Formula: see text] with [Formula: see text]. Then [Formula: see text] is almost additive on [Formula: see text], that is, [Formula: see text] Moreover, there exist an additive derivation [Formula: see text] of [Formula: see text] and a nonlinear map [Formula: see text] such that [Formula: see text] for [Formula: see text], where [Formula: see text] for any [Formula: see text] with [Formula: see text].
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