Differential inequalities for spirallike and strongly starlike functions

Abstract In this paper, by using a technique of the first-order differential subordination, we find several sufficient conditions for an analytic function p such that p ( 0 ) = 1 $p(0)=1$ to satisfy Re { e i β p ( z ) } > γ $\operatorname{Re}\{ {\mathrm{e}}^{{\mathrm{i}}\beta } p(z) \} > \gamm...

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Autores principales:	Nak Eun Cho, Oh Sang Kwon, Young Jae Sim
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Carathéodory functions Differential subordination Starlike functions Spirallike functions Strongly starlike functions Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/b19d43a2ac9249b9ba0851a6e8e3aa3b
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spelling	oai:doaj.org-article:b19d43a2ac9249b9ba0851a6e8e3aa3b2021-12-05T12:07:10ZDifferential inequalities for spirallike and strongly starlike functions10.1186/s13662-021-03670-91687-1847https://doaj.org/article/b19d43a2ac9249b9ba0851a6e8e3aa3b2021-11-01T00:00:00Zhttps://doi.org/10.1186/s13662-021-03670-9https://doaj.org/toc/1687-1847Abstract In this paper, by using a technique of the first-order differential subordination, we find several sufficient conditions for an analytic function p such that p ( 0 ) = 1 $p(0)=1$ to satisfy Re { e i β p ( z ) } > γ $\operatorname{Re}\{ {\mathrm{e}}^{{\mathrm{i}}\beta } p(z) \} > \gamma $ or \| arg { p ( z ) − γ } \| < δ $\| \arg \{p(z)-\gamma \} \|<\delta $ for all z ∈ D $z\in \mathbb{D}$ , where β ∈ ( − π / 2 , π / 2 ) $\beta \in (-\pi /2,\pi /2)$ , γ ∈ [ 0 , cos β ) $\gamma \in [0,\cos \beta )$ , δ ∈ ( 0 , 1 ] $\delta \in (0,1]$ and D : = { z ∈ C : \| z \| < 1 } $\mathbb{D}:=\{z\in \mathbb{C}:\|z\|<1 \}$ . The results obtained here will be applied to find some conditions for spirallike functions and strongly starlike functions in D $\mathbb{D}$ .Nak Eun ChoOh Sang KwonYoung Jae SimSpringerOpenarticleCarathéodory functionsDifferential subordinationStarlike functionsSpirallike functionsStrongly starlike functionsMathematicsQA1-939ENAdvances in Difference Equations, Vol 2021, Iss 1, Pp 1-12 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Carathéodory functions Differential subordination Starlike functions Spirallike functions Strongly starlike functions Mathematics QA1-939
spellingShingle	Carathéodory functions Differential subordination Starlike functions Spirallike functions Strongly starlike functions Mathematics QA1-939 Nak Eun Cho Oh Sang Kwon Young Jae Sim Differential inequalities for spirallike and strongly starlike functions
description	Abstract In this paper, by using a technique of the first-order differential subordination, we find several sufficient conditions for an analytic function p such that p ( 0 ) = 1 $p(0)=1$ to satisfy Re { e i β p ( z ) } > γ $\operatorname{Re}\{ {\mathrm{e}}^{{\mathrm{i}}\beta } p(z) \} > \gamma $ or \| arg { p ( z ) − γ } \| < δ $\| \arg \{p(z)-\gamma \} \|<\delta $ for all z ∈ D $z\in \mathbb{D}$ , where β ∈ ( − π / 2 , π / 2 ) $\beta \in (-\pi /2,\pi /2)$ , γ ∈ [ 0 , cos β ) $\gamma \in [0,\cos \beta )$ , δ ∈ ( 0 , 1 ] $\delta \in (0,1]$ and D : = { z ∈ C : \| z \| < 1 } $\mathbb{D}:=\{z\in \mathbb{C}:\|z\|<1 \}$ . The results obtained here will be applied to find some conditions for spirallike functions and strongly starlike functions in D $\mathbb{D}$ .
format	article
author	Nak Eun Cho Oh Sang Kwon Young Jae Sim
author_facet	Nak Eun Cho Oh Sang Kwon Young Jae Sim
author_sort	Nak Eun Cho
title	Differential inequalities for spirallike and strongly starlike functions
title_short	Differential inequalities for spirallike and strongly starlike functions
title_full	Differential inequalities for spirallike and strongly starlike functions
title_fullStr	Differential inequalities for spirallike and strongly starlike functions
title_full_unstemmed	Differential inequalities for spirallike and strongly starlike functions
title_sort	differential inequalities for spirallike and strongly starlike functions
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/b19d43a2ac9249b9ba0851a6e8e3aa3b
work_keys_str_mv	AT nakeuncho differentialinequalitiesforspirallikeandstronglystarlikefunctions AT ohsangkwon differentialinequalitiesforspirallikeandstronglystarlikefunctions AT youngjaesim differentialinequalitiesforspirallikeandstronglystarlikefunctions
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Differential inequalities for spirallike and strongly starlike functions

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