On the analog of the Sălăgean class for Dirichlet series and the solutions of one linear differential equation with exponential coefficients - Sheremeta, M.; Mulyava, O.; Medvedev, M. (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 517.537In his study of the geometric properties of functions analytic in a disk ${\mathbb D} = \{z\colon |z| \alpha\in [0, 1)$ for each $ z\in{\mathbb D},$ where $D^jf$ is the Sălăgean derivative. For Dirichlet series $F(s) = e^{s}-\sum _{k = 1 }^{\infty}f_k\exp\{s\lambda_k\}$ with $f_k\ge0$ absolutely convergent in the half plane $\Pi_0 = \{s\colon \operatorname{Re} s \alpha$ for each $s\in \Pi_0.$ By analogy with the neighborhood of an analytic function in ${\mathbb D}$ defined by A. V. Goodman, for $F\in D_{j}(\alpha),$ we introduce the concept of a neighborhood $O_{j,\delta}(F)$ and establish the conditions under which all functions from $O_{j,\delta}(F)$ belong to $D_{j}(\alpha_1),$ $0\le \alpha_1