The authors use a comparison theorem due to Hethcote to establish asymptotic inequalities for the zeros of the Airy functions Ai(x) and Bi(x). They consider the differential equation
satisfied by (( and and the differential equation
satisfied by . Then the authors compare (1) and (2) when g() is chosen in such a way that (1) and (2) are “very close”.
This reviewer observes that this idea is not original. Several applications of this idea have been given by L. Gatteschi [see, for example, L. Gatteschi, SIAM J. Math. Anal. 18, 1549-1562 (1987; Zbl 0639.33012)]. No mention is made by the authors of Gatteschi’s papers.