Monotonicity of the ratio of modified Bessel functions of the first kind with applications.

Let [Formula: see text] with [Formula: see text] be the modified Bessel functions of the first kind of order . In this paper, we prove the monotonicity of the function [Formula: see text] on [Formula: see text] for different values of parameter with [Formula: see text]. As applications, we deduce some new Simpson-Spector-type inequalities for [Formula: see text] and derive a new type of bounds [Formula: see text] ([Formula: see text]) for [Formula: see text]. In particular, we show that the upper bound [Formula: see text] for [Formula: see text] is the minimum over all upper bounds [Formula: see text], where [Formula: see text] and is not comparable with other sharpest upper bounds. We also find such type of upper bounds for [Formula: see text] with [Formula: see text] and for [Formula: see text] with [Formula: see text].