Functional inequalities involving special functions

Let up(x) be the generalized and normalized Bessel function depending on parameters b, c,p and let σ(r) = up(1 − r2)/up(r2), r ∈ (0, 1). Motivated by an open problem of Anderson, Vamanamurthy, and Vuorinen we prove that √σ(r1)σ (r2) σ(√r1r2) for all r1, r2 ∈ (0, 1) for certain conditions on the parameters b, c,p. © 2005 Elsevier Inc. All rights reserved.