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 for all r1,r2∈(0,1) for certain conditions on the parameters b,c,p.