On approximating the modified Bessel function of the second kind

In the article, we prove that the double inequalities [GRAPHIC] hold for all x > 0 if and only if a >= 1/4 and b = 0 if a, b is an element of[0,infinity), where K-nu(x) is the modified Bessel function of the second kind. As applications, we provide bounds for Kn+1(x)/K-n(x) with n is an element of N and present the necessary and sufficient condition such that the function [GRAPHIC] is strictly increasing (decreasing) on (0,infinity).