Bounds for Zeros of Some Special Functions

For let and be zeros (ordered by increasing values) of and , respectively, which are non-trivial solutions of <!-- MATH $u'' + p(x)u = 0$ --> and <!-- MATH $v'' + q(x)v = 0$ --> with continuous and . It is shown that if <!-- MATH ${b_n} - {c_n} \to 0$ --> as <!-- MATH $n \to \infty ,\;p(x) \geqq q(x)$ --> , and either or is nonincreasing, then <!-- MATH ${b_n} \geqq {c_n}$ --> for . Inequalities related to asymptotic expansions are obtained for the negative zeros of the Airy function and the zeros of the Bessel function .