For denote, as usual, by , , , , the -th positive zeros of the Bessel functions , of the first and second kind and their derivatives , , respectively. Let be the -th positive zero of the cylinder function , , . By using the notation introduced in two earlier papers [SIAM, J. Math. Anal. 15, 206-212 (1984; Zbl 0541.33001); Stud. Sci. Math. Hung. 25, 377-385 (1990; Zbl 0748.33002)], the authors define by , with , and similarly to denote the zeros of defined in such a way that . In the present paper they prove the following results:
Theorem 1. For the zeros of the cylinder function the inequalities , , hold.
Theorem 2. For the zeros of the cylinder function and for the zeros of satisfying the relation , the inequality for , holds.