Abstract
1. In a previous note [1], the strong differential, a variant of the classical Frechet differential, was defined. Strong differentiability at a point seems to be a good smoothness condition for related function theorems, being stronger than the insufficient condition of Frechet differentiability at the point and weaker than Frechet differentiability in a neighborhood of the point, together with continuity of the differential at the point. In this note we state as a lemma a slight generalization of the theorem of [1]. Algebraic manipulation of the relations involved then enables us to extend the range over which the conclusion of the lemma is valid.
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