Let [Formula: see text] with [Formula: see text] be the modified Bessel functions of the first kind of order v. In this paper, we prove the monotonicity of the function [Formula: see text] on [Formula: see text] for different values of parameter p with [Formula: see text]. As applications, we deduce some new Simpson-Spector-type inequalities for [Formula: see text] and derive a new type of boun...