Certain inequalities for the modified Bessel-type function

Abstract

We establish some new inequalities for the modified Bessel-type function λ (β) ν,σ (x) studied by Glaeske et al. [in J. Comput. Appl. Math. 118(1-2):151-168, 2000] as the kernel of an integral transformation that modifies Krätzel's integral transformation. The inequalities obtained are closely related to the generalized Hurwitz-Lerch zeta function and complementary incomplete gamma function. We also deduce some useful inequalities for the modified Bessel function of the second kind K ν (x) and Mills' ratio M(x) as worthwhile applications of our main results.