Results 1 to 8 of about 13 (8)

Pseudostarlikeness and Pseudoconvexity of Multiple Dirichlet Series

Universal Journal of Mathematics and Applications, 2023
Let $p\in {\Bbb N}$, $s=(s_1,\ldots,s_p)\in {\Bbb C}^p$, $h=(h_1,\ldots,h_p)\in {\Bbb R}^p_+$, $(n)=(n_1,\ldots,n_p)\in {\Bbb N}^p$ and the sequences $\lambda_{(n)}=(\lambda^{(1)}_{n_1},\ldots,\lambda^{(p)}_{n_p})$ are such that $0<\lambda^{(j)}_1 ...
Myroslav Sheremeta
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On Dirichlet series similar to Hadamard compositions in half-plane [PDF]

Karpatsʹkì Matematičnì Publìkacìï, 2023
Let $F(s)=\sum\limits_{n=1}^{\infty}a_n\exp\{s\lambda_n\}$ and $F_j(s)=\sum\limits_{n=1}^{\infty}a_{n,j}\exp\{s\lambda_n\},$ $j=\overline{1,p},$ be Dirichlet series with exponents $0\le\lambda_n\uparrow+\infty,$ $n\to\infty,$ and the abscissas of ...
A.I. Bandura, O.M. Mulyava, M.M. Sheremeta   +2 more
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Pseudostarlike and pseudoconvex solutions of a differential equation with exponential coefficients

Математичні Студії, 2021
Dirichlet series $F(s)=e^{s}+\sum_{k=1}^{\infty}f_ke^{s\lambda_k}$ with the exponents ...
M.M. Sheremeta
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Pseudostarlike and pseudoconvex in a direction multiple Dirichlet series

Математичні Студії, 2023
The article introduces the concepts of pseudostarlikeness and pseudoconvexity in the direction of absolutely converges in $\Pi_0=\{s\in\mathbb{C}^p\colon \text{Re}\,sh$, $\text{Re ...
M. M. Sheremeta, O. B. Skaskiv
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Pseudostarlike and pseudoconvex Dirichlet series of the order $\alpha$ and the type $\beta$

Математичні Студії, 2020
The concepts of the pseudostarlikeness of order $\alpha\in [0,\,1)$ and type $\beta\in (0,\,1]$ and the pseudoconvexity of order $\alpha$ and type $\beta$ are introduced for Dirichlet series with null abscissa of absolute convergence.
M.M. Sheremeta
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ELEMENTARY NOTES ON α-PSEUDOSTARLIKE DIRICHLET SERIES

Visnyk Lvivskogo Universytetu Seriya Mekhaniko-Matematychna
A Dirichlet series F(s)=esλ1+∑k=2∞fkexp{sλk},0<λk↑∞, that converges absolutely in the half-plane Π0 = {s : Res < 0}, is said to be α-pseudostarlike, α ∈ R, if Re{(1 − α)F′(s)/F(s) + αF′′(s)/F′(s)}> 0, s ∈ Π0. It is proved that each α-pseudostarlike function is pseudostarlike, that is Re{F′(s)/F(s)} > 0 for all s ∈ Π0.
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ON PSEUDOSTARLIKE AND PSEUDOCONVEX DIRICHLET SERIES

Bukovinian Mathematical Journal, 2021
The concepts of the pseudostarlikeness of order $\alpha\in [0,\,1)$ and type $\beta\in (0,\,1]$ and the pseudoconvexity of the order $\alpha$ and type $\beta$ are introduced for Dirichlet series of the form $F(s)=e^{-sh}+\sum_{j=1}^{n}a_j\exp\{-sh_j\}+\sum_{k=1}^{\infty}f_k\exp\{s\lambda_k\}$, where $h>h_n>\dots>h_1\ge 1$ and $(\lambda_k)$ is ...
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Pseudostarlike, Pseudoconvex, and Close-to-Pseudoconvex Dirichlet Series Satisfying Differential Equations with Exponential Coefficients

Journal of Mathematical Sciences, 2020
The concepts of pseudostarlikeness, pseudoconvexity, and closeness to pseudoconvexity are introduced for the Dirichlet series with the null abscissa of absolute convergence. The obtained results are used to study the properties of solutions of the differential equations with exponential coefficients.
O. M. Holovata, O. M. Mulyava, M. M. Sheremeta   +2 more
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