On a class of slowly changing functions (Q1122013)

The paper is devoted to the asymptotic properties of differentiable functions \(J(r)\geq 0,\quad r\geq 0,\) which satisfy the condition \((r \log r)J'(r)/J(r)\to 0,\quad r\to \infty.\) The change of variable \(r=\log t\) maps the class under consideration onto the class of differentiable functions which are slowly changing in the sense of Karamata. Some applications to the study of growth and distribution of zeros of entire functions are given.