another look at inheritance of uniform continuity of 1-dimensional aggregation functions by their super-additive transformations

In an earlier paper by seliga, siran and the second author (j. mahani math. res. center 8 (2019) 37–51) on lifting continuity properties of aggregation functions to their super- and sub-additive transformations it was shown that uniform continuity is preserved by super-additive transformations in dimension 1. we give a shorter and more direct proof of this result and of a related linear bound on uniformly continuous aggregation functions.