Relations of a planar domains bounded by hyperbolas with families of holomorphic functions

Autor:	Stanisława Kanas, Ali Ebadian, Vali Soltani Masih
Jazyk:	angličtina
Rok vydání:	2019
Předmět:	Applied Mathematics lcsh:Mathematics Holomorphic function A domain Subordination Domain bounded by hyperbola lcsh:QA1-939 Hyperbola Starlike and convex functions Combinatorics Planar Bounded function Pi Discrete Mathematics and Combinatorics Analysis Univalent functions Mathematics
Zdroj:	Journal of Inequalities and Applications, Vol 2019, Iss 1, Pp 1-14 (2019)
DOI:	10.1186/s13660-019-2190-8
Popis:	We consider a family of analytic and normalized functions with the property that $zf'(z)/f(z)$ z f ′ ( z ) / f ( z ) (or $1+zf''(z)/f'(z)$ 1 + z f ″ ( z ) / f ′ ( z ) ) lies in a domain bounded by a right branch of a hyperbola $\rho =\rho (s)= ( 2 \cos \frac{\varphi }{s} )^{-s}$ ρ = ρ ( s ) = ( 2 cos φ s ) − s , where $0< s\le 1$ 0 < s ≤ 1 and $|\varphi | | φ | < ( π s ) / 2 . A comprehensive characteristic of that families and relations with the well known families of univalent functions are presented. Some relevant examples are indicated.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fea05b155d0e1f04892a189287d1e57c http://link.springer.com/article/10.1186/s13660-019-2190-8 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
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