On certain subclasses of close-to-convex functions related with the second-order differential subordination
Let $\mathcal{A}$ be the family of analytic and normalized functions in the open unit disc $|z|
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| creator | Mahzoon, Hesam Kargar, Rahim |
| description | Let $\mathcal{A}$ be the family of analytic and normalized functions in the
open unit disc $|z| |
| doi_str_mv | 10.48550/arxiv.1901.02670 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_1901_02670</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1901_02670</sourcerecordid><originalsourceid>FETCH-LOGICAL-a670-51483201c59476562725f31f4f9dccd449529aa5380698e4e8e9c70160f877d53</originalsourceid><addsrcrecordid>eNotj89OAyEYxLl4MNUH8CQvQIVdWOBoGv8lTXrpffMJHylxBQO01rd3t3qaZDIzmR8hd4KvpVGKP0A5x9NaWC7WvBs0vyYfu0QdlgYx0Xp8dxPUipXmQN2UK7KWmcvphGcajsm1mFOlBSdo6Ol3bAfaDkgrzhnPcvFYqI8hYMHUIkzL5OzGBEvzhlwFmCre_uuK7J-f9ptXtt29vG0etwzmS0wJafqOC6es1IMaOt2p0Isgg_XOeSmt6iyA6g0frEGJBq3TXAw8GK296lfk_m_2Qjt-lfgJ5WdcqMcLdf8LZzNTag</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>On certain subclasses of close-to-convex functions related with the second-order differential subordination</title><source>arXiv.org</source><creator>Mahzoon, Hesam ; Kargar, Rahim</creator><creatorcontrib>Mahzoon, Hesam ; Kargar, Rahim</creatorcontrib><description><![CDATA[Let $\mathcal{A}$ be the family of analytic and normalized functions in the
open unit disc $|z|<1$. In this article we consider the following classes
\begin{equation*}
\mathcal{R}(\alpha,\beta):=\left\{ f\in \mathcal{A}: {\rm
Re}\left\{f'(z)+\frac{1+e^{i\alpha}}{2}zf''(z)\right\}>\beta,\, |z|<1\right\}
\end{equation*} and \begin{equation*}
\mathcal{L}_\alpha(b):=\left\{f\in\mathcal{A}:\left|f'(z)
+\frac{1+e^{i\alpha}}{2}zf''(z)-b\right|< b,\, |z|<1 \right\},
\end{equation*} where $-\pi<\alpha\leq \pi$, $0\leq \beta<1$ and $b>1/2$. We
show that if $f\in \mathcal{R}(\alpha,\beta)$, then ${\rm Re}\{f'(z)\}$ and
${\rm Re}\{f(z)/z\}$ are greater than $\beta$, and if
$f\in\mathcal{L}_\alpha(b)$, then $0<{\rm Re}\{f'(z)\}<2b$. Also, some another
interesting properties of the class $\mathcal{L}_\alpha(b)$ are investigated.
Finally, the radius of univalence of 2-th section sum of $f\in
\mathcal{R}(\alpha,\beta)$ is obtained.]]></description><identifier>DOI: 10.48550/arxiv.1901.02670</identifier><language>eng</language><subject>Mathematics - Complex Variables</subject><creationdate>2019-01</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1901.02670$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1901.02670$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Mahzoon, Hesam</creatorcontrib><creatorcontrib>Kargar, Rahim</creatorcontrib><title>On certain subclasses of close-to-convex functions related with the second-order differential subordination</title><description><![CDATA[Let $\mathcal{A}$ be the family of analytic and normalized functions in the
open unit disc $|z|<1$. In this article we consider the following classes
\begin{equation*}
\mathcal{R}(\alpha,\beta):=\left\{ f\in \mathcal{A}: {\rm
Re}\left\{f'(z)+\frac{1+e^{i\alpha}}{2}zf''(z)\right\}>\beta,\, |z|<1\right\}
\end{equation*} and \begin{equation*}
\mathcal{L}_\alpha(b):=\left\{f\in\mathcal{A}:\left|f'(z)
+\frac{1+e^{i\alpha}}{2}zf''(z)-b\right|< b,\, |z|<1 \right\},
\end{equation*} where $-\pi<\alpha\leq \pi$, $0\leq \beta<1$ and $b>1/2$. We
show that if $f\in \mathcal{R}(\alpha,\beta)$, then ${\rm Re}\{f'(z)\}$ and
${\rm Re}\{f(z)/z\}$ are greater than $\beta$, and if
$f\in\mathcal{L}_\alpha(b)$, then $0<{\rm Re}\{f'(z)\}<2b$. Also, some another
interesting properties of the class $\mathcal{L}_\alpha(b)$ are investigated.
Finally, the radius of univalence of 2-th section sum of $f\in
\mathcal{R}(\alpha,\beta)$ is obtained.]]></description><subject>Mathematics - Complex Variables</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj89OAyEYxLl4MNUH8CQvQIVdWOBoGv8lTXrpffMJHylxBQO01rd3t3qaZDIzmR8hd4KvpVGKP0A5x9NaWC7WvBs0vyYfu0QdlgYx0Xp8dxPUipXmQN2UK7KWmcvphGcajsm1mFOlBSdo6Ol3bAfaDkgrzhnPcvFYqI8hYMHUIkzL5OzGBEvzhlwFmCre_uuK7J-f9ptXtt29vG0etwzmS0wJafqOC6es1IMaOt2p0Isgg_XOeSmt6iyA6g0frEGJBq3TXAw8GK296lfk_m_2Qjt-lfgJ5WdcqMcLdf8LZzNTag</recordid><startdate>20190109</startdate><enddate>20190109</enddate><creator>Mahzoon, Hesam</creator><creator>Kargar, Rahim</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20190109</creationdate><title>On certain subclasses of close-to-convex functions related with the second-order differential subordination</title><author>Mahzoon, Hesam ; Kargar, Rahim</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a670-51483201c59476562725f31f4f9dccd449529aa5380698e4e8e9c70160f877d53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Mathematics - Complex Variables</topic><toplevel>online_resources</toplevel><creatorcontrib>Mahzoon, Hesam</creatorcontrib><creatorcontrib>Kargar, Rahim</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Mahzoon, Hesam</au><au>Kargar, Rahim</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On certain subclasses of close-to-convex functions related with the second-order differential subordination</atitle><date>2019-01-09</date><risdate>2019</risdate><abstract><![CDATA[Let $\mathcal{A}$ be the family of analytic and normalized functions in the
open unit disc $|z|<1$. In this article we consider the following classes
\begin{equation*}
\mathcal{R}(\alpha,\beta):=\left\{ f\in \mathcal{A}: {\rm
Re}\left\{f'(z)+\frac{1+e^{i\alpha}}{2}zf''(z)\right\}>\beta,\, |z|<1\right\}
\end{equation*} and \begin{equation*}
\mathcal{L}_\alpha(b):=\left\{f\in\mathcal{A}:\left|f'(z)
+\frac{1+e^{i\alpha}}{2}zf''(z)-b\right|< b,\, |z|<1 \right\},
\end{equation*} where $-\pi<\alpha\leq \pi$, $0\leq \beta<1$ and $b>1/2$. We
show that if $f\in \mathcal{R}(\alpha,\beta)$, then ${\rm Re}\{f'(z)\}$ and
${\rm Re}\{f(z)/z\}$ are greater than $\beta$, and if
$f\in\mathcal{L}_\alpha(b)$, then $0<{\rm Re}\{f'(z)\}<2b$. Also, some another
interesting properties of the class $\mathcal{L}_\alpha(b)$ are investigated.
Finally, the radius of univalence of 2-th section sum of $f\in
\mathcal{R}(\alpha,\beta)$ is obtained.]]></abstract><doi>10.48550/arxiv.1901.02670</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Complex Variables |
| title | On certain subclasses of close-to-convex functions related with the second-order differential subordination |
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