In his study of the geometric properties of functions analytic in a disk \({\mathbb{D}}\) = {z : |z| < 1}, G. S. Sălăgean introduced a class Sj(α) of functions f(z) = \(z+{\sum }_{k=2}^{\infty }{f}_{k}{z}^{k}\) such that \(\mathrm{Re}\frac{{D}^{j+1}f\left(z\right)}{{D}^{j}f\left(z\right)}\) > α ∈ [0, 1) for each z ∈ \({\mathbb{D}}\) , where D j f is the Sălăgean derivative. For Dirichlet series F(s) = es – \({\sum }_{k=1}^{\infty }{f}_{k}\mathrm{exp}\left\{{s\lambda }_{k}\right\}\) with fk ≥ 0 absolutely convergent in the half plane Π0 = {s : Re s < 0}, the role of an analog of the Sălăgean class is played by the class Dj(α) specified by the condition \(\mathrm{Re}\frac{{F}^{\left(j+1\right)}\left(s\right)}{{F}^{\left(j\right)}\left(s\right)}\) > α for each s ∈ Π0. By analogy with the neighborhood of an analytic function in \({\mathbb{D}}\) defined by A.V. Goodman, for F ∈ Dj(α), we introduce the concept of a neighborhood Oj,δ(F) and establish conditions under which all functions from Oj,δ(F) belong to Dj(α1), 0 ≤ α1 < α < 1, and vice versa. The problem of belonging of solutions of the differential equation \(\frac{{d}^{2}w}{{ds}^{2}}\) + (γ0e2s + γ1es + γ2)w = 0 with real parameters to the class Dj(α) is analyzed.
