On the Monotony of Bessel Functions of the First Kind

Let J(p) denote the Bessel function of the first kind. In Baricz and Andras (Complex Var. Elliptic Equ. 54(7):689-696, 2009) the authors deduced a kind of monotony for a normalized form of the Bessel function J(p). They proved using integral representations that the inequalities -1/4 < q < p imply J(p)(U) subset of J(q)(U), (1) where J(p) is a normalized form of J(p). In Baricz and Andras (2009) it is conjectured that the weaker condition-1 < q < p implies the inclusion (1) too. This paper shows that an approach based on subordination factor sequences leads to the desired result.