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On the Coefficients of Certain Subclasses of Harmonic Univalent Mappings with Nonzero Pole
Let Co ( p ), p ∈ ( 0 , 1 ] be the class of all meromorphic univalent functions φ defined in the open unit disc D with normalizations φ ( 0 ) = 0 = φ ′ ( 0 ) - 1 and having simple pole at z = p ∈ ( 0 , 1 ] such that the complement of φ ( D ) is a convex domain. The class Co ( p ) is called the class...
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| Published in: | Boletim da Sociedade Brasileira de Matemática 2021-12, Vol.52 (4), p.1041-1053 |
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| cites | cdi_FETCH-LOGICAL-c319t-3e2f8197d2557ca87b2a496a6e6eb8e25527eb8d8aa00d080811a2bd06cb428d3 |
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| container_title | Boletim da Sociedade Brasileira de Matemática |
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| creator | Bhowmik, Bappaditya Majee, Santana |
| description | Let
Co
(
p
),
p
∈
(
0
,
1
]
be the class of all meromorphic univalent functions
φ
defined in the open unit disc
D
with normalizations
φ
(
0
)
=
0
=
φ
′
(
0
)
-
1
and having simple pole at
z
=
p
∈
(
0
,
1
]
such that the complement of
φ
(
D
)
is a convex domain. The class
Co
(
p
) is called the class of concave univalent functions. Let
S
H
0
(
p
)
be the class of all sense preserving univalent harmonic mappings
f
defined on
D
having simple pole at
z
=
p
∈
(
0
,
1
)
with the normalizations
f
(
0
)
=
f
z
(
0
)
-
1
=
0
and
f
z
¯
(
0
)
=
0
. We first derive the exact regions of variability for the second Taylor coefficients of
h
where
f
=
h
+
g
¯
∈
S
H
0
(
p
)
with
h
-
g
∈
C
o
(
p
)
. Next we consider the class
S
H
0
(
1
)
of all sense preserving univalent harmonic mappings
f
in
D
having simple pole at
z
=
1
with the same normalizations as above. We derive exact regions of variability for the coefficients of
h
where
f
=
h
+
g
¯
∈
S
H
0
(
1
)
satisfying
h
-
e
2
i
θ
g
∈
C
o
(
1
)
with dilatation
g
′
(
z
)
/
h
′
(
z
)
=
e
-
2
i
θ
z
, for some
θ
,
0
≤
θ
<
π
. |
| doi_str_mv | 10.1007/s00574-021-00244-x |
| format | article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2582804863</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2582804863</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-3e2f8197d2557ca87b2a496a6e6eb8e25527eb8d8aa00d080811a2bd06cb428d3</originalsourceid><addsrcrecordid>eNp9kM1OwzAQhC0EEqXwApwscQ6sHSd2jygCilR-JOiFi-UkTusqtYOdQuHpMQ2IG6cdjb6ZlQahUwLnBIBfBICMswQoSQAoY8l2D41IzkXCOWH7vzpj7BAdhbACgDzL0hF6ebC4X2pcON00pjLa9gG7Bhfa98pY_LQpq1aFoHfuVPm1s6bCc2veVBthfKe6zthFwO-mX-J7Zz-1d_jRtfoYHTSqDfrk547R_PrquZgms4eb2-JyllQpmfRJqmkjyITXNMt4pQQvqWKTXOU616XQ0aU8ilooBVCDAEGIomUNeVUyKup0jM6G3s67140OvVy5jbfxpaSZoAKYyNNI0YGqvAvB60Z23qyV_5AE5PeGcthQxg3lbkO5jaF0CIUI24X2f9X_pL4AR9x06A</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2582804863</pqid></control><display><type>article</type><title>On the Coefficients of Certain Subclasses of Harmonic Univalent Mappings with Nonzero Pole</title><source>Springer Nature</source><creator>Bhowmik, Bappaditya ; Majee, Santana</creator><creatorcontrib>Bhowmik, Bappaditya ; Majee, Santana</creatorcontrib><description>Let
Co
(
p
),
p
∈
(
0
,
1
]
be the class of all meromorphic univalent functions
φ
defined in the open unit disc
D
with normalizations
φ
(
0
)
=
0
=
φ
′
(
0
)
-
1
and having simple pole at
z
=
p
∈
(
0
,
1
]
such that the complement of
φ
(
D
)
is a convex domain. The class
Co
(
p
) is called the class of concave univalent functions. Let
S
H
0
(
p
)
be the class of all sense preserving univalent harmonic mappings
f
defined on
D
having simple pole at
z
=
p
∈
(
0
,
1
)
with the normalizations
f
(
0
)
=
f
z
(
0
)
-
1
=
0
and
f
z
¯
(
0
)
=
0
. We first derive the exact regions of variability for the second Taylor coefficients of
h
where
f
=
h
+
g
¯
∈
S
H
0
(
p
)
with
h
-
g
∈
C
o
(
p
)
. Next we consider the class
S
H
0
(
1
)
of all sense preserving univalent harmonic mappings
f
in
D
having simple pole at
z
=
1
with the same normalizations as above. We derive exact regions of variability for the coefficients of
h
where
f
=
h
+
g
¯
∈
S
H
0
(
1
)
satisfying
h
-
e
2
i
θ
g
∈
C
o
(
1
)
with dilatation
g
′
(
z
)
/
h
′
(
z
)
=
e
-
2
i
θ
z
, for some
θ
,
0
≤
θ
<
π
.</description><identifier>ISSN: 1678-7544</identifier><identifier>EISSN: 1678-7714</identifier><identifier>DOI: 10.1007/s00574-021-00244-x</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Coefficients ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Theoretical</subject><ispartof>Boletim da Sociedade Brasileira de Matemática, 2021-12, Vol.52 (4), p.1041-1053</ispartof><rights>Sociedade Brasileira de Matemática 2021</rights><rights>Sociedade Brasileira de Matemática 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-3e2f8197d2557ca87b2a496a6e6eb8e25527eb8d8aa00d080811a2bd06cb428d3</citedby><cites>FETCH-LOGICAL-c319t-3e2f8197d2557ca87b2a496a6e6eb8e25527eb8d8aa00d080811a2bd06cb428d3</cites><orcidid>0000-0001-9171-3548</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Bhowmik, Bappaditya</creatorcontrib><creatorcontrib>Majee, Santana</creatorcontrib><title>On the Coefficients of Certain Subclasses of Harmonic Univalent Mappings with Nonzero Pole</title><title>Boletim da Sociedade Brasileira de Matemática</title><addtitle>Bull Braz Math Soc, New Series</addtitle><description>Let
Co
(
p
),
p
∈
(
0
,
1
]
be the class of all meromorphic univalent functions
φ
defined in the open unit disc
D
with normalizations
φ
(
0
)
=
0
=
φ
′
(
0
)
-
1
and having simple pole at
z
=
p
∈
(
0
,
1
]
such that the complement of
φ
(
D
)
is a convex domain. The class
Co
(
p
) is called the class of concave univalent functions. Let
S
H
0
(
p
)
be the class of all sense preserving univalent harmonic mappings
f
defined on
D
having simple pole at
z
=
p
∈
(
0
,
1
)
with the normalizations
f
(
0
)
=
f
z
(
0
)
-
1
=
0
and
f
z
¯
(
0
)
=
0
. We first derive the exact regions of variability for the second Taylor coefficients of
h
where
f
=
h
+
g
¯
∈
S
H
0
(
p
)
with
h
-
g
∈
C
o
(
p
)
. Next we consider the class
S
H
0
(
1
)
of all sense preserving univalent harmonic mappings
f
in
D
having simple pole at
z
=
1
with the same normalizations as above. We derive exact regions of variability for the coefficients of
h
where
f
=
h
+
g
¯
∈
S
H
0
(
1
)
satisfying
h
-
e
2
i
θ
g
∈
C
o
(
1
)
with dilatation
g
′
(
z
)
/
h
′
(
z
)
=
e
-
2
i
θ
z
, for some
θ
,
0
≤
θ
<
π
.</description><subject>Coefficients</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Theoretical</subject><issn>1678-7544</issn><issn>1678-7714</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kM1OwzAQhC0EEqXwApwscQ6sHSd2jygCilR-JOiFi-UkTusqtYOdQuHpMQ2IG6cdjb6ZlQahUwLnBIBfBICMswQoSQAoY8l2D41IzkXCOWH7vzpj7BAdhbACgDzL0hF6ebC4X2pcON00pjLa9gG7Bhfa98pY_LQpq1aFoHfuVPm1s6bCc2veVBthfKe6zthFwO-mX-J7Zz-1d_jRtfoYHTSqDfrk547R_PrquZgms4eb2-JyllQpmfRJqmkjyITXNMt4pQQvqWKTXOU616XQ0aU8ilooBVCDAEGIomUNeVUyKup0jM6G3s67140OvVy5jbfxpaSZoAKYyNNI0YGqvAvB60Z23qyV_5AE5PeGcthQxg3lbkO5jaF0CIUI24X2f9X_pL4AR9x06A</recordid><startdate>20211201</startdate><enddate>20211201</enddate><creator>Bhowmik, Bappaditya</creator><creator>Majee, Santana</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-9171-3548</orcidid></search><sort><creationdate>20211201</creationdate><title>On the Coefficients of Certain Subclasses of Harmonic Univalent Mappings with Nonzero Pole</title><author>Bhowmik, Bappaditya ; Majee, Santana</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-3e2f8197d2557ca87b2a496a6e6eb8e25527eb8d8aa00d080811a2bd06cb428d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Coefficients</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bhowmik, Bappaditya</creatorcontrib><creatorcontrib>Majee, Santana</creatorcontrib><collection>CrossRef</collection><jtitle>Boletim da Sociedade Brasileira de Matemática</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bhowmik, Bappaditya</au><au>Majee, Santana</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Coefficients of Certain Subclasses of Harmonic Univalent Mappings with Nonzero Pole</atitle><jtitle>Boletim da Sociedade Brasileira de Matemática</jtitle><stitle>Bull Braz Math Soc, New Series</stitle><date>2021-12-01</date><risdate>2021</risdate><volume>52</volume><issue>4</issue><spage>1041</spage><epage>1053</epage><pages>1041-1053</pages><issn>1678-7544</issn><eissn>1678-7714</eissn><abstract>Let
Co
(
p
),
p
∈
(
0
,
1
]
be the class of all meromorphic univalent functions
φ
defined in the open unit disc
D
with normalizations
φ
(
0
)
=
0
=
φ
′
(
0
)
-
1
and having simple pole at
z
=
p
∈
(
0
,
1
]
such that the complement of
φ
(
D
)
is a convex domain. The class
Co
(
p
) is called the class of concave univalent functions. Let
S
H
0
(
p
)
be the class of all sense preserving univalent harmonic mappings
f
defined on
D
having simple pole at
z
=
p
∈
(
0
,
1
)
with the normalizations
f
(
0
)
=
f
z
(
0
)
-
1
=
0
and
f
z
¯
(
0
)
=
0
. We first derive the exact regions of variability for the second Taylor coefficients of
h
where
f
=
h
+
g
¯
∈
S
H
0
(
p
)
with
h
-
g
∈
C
o
(
p
)
. Next we consider the class
S
H
0
(
1
)
of all sense preserving univalent harmonic mappings
f
in
D
having simple pole at
z
=
1
with the same normalizations as above. We derive exact regions of variability for the coefficients of
h
where
f
=
h
+
g
¯
∈
S
H
0
(
1
)
satisfying
h
-
e
2
i
θ
g
∈
C
o
(
1
)
with dilatation
g
′
(
z
)
/
h
′
(
z
)
=
e
-
2
i
θ
z
, for some
θ
,
0
≤
θ
<
π
.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00574-021-00244-x</doi><tpages>13</tpages><orcidid>https://orcid.org/0000-0001-9171-3548</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1678-7544 |
| ispartof | Boletim da Sociedade Brasileira de Matemática, 2021-12, Vol.52 (4), p.1041-1053 |
| issn | 1678-7544 1678-7714 |
| language | eng |
| recordid | cdi_proquest_journals_2582804863 |
| source | Springer Nature |
| subjects | Coefficients Mathematical and Computational Physics Mathematics Mathematics and Statistics Theoretical |
| title | On the Coefficients of Certain Subclasses of Harmonic Univalent Mappings with Nonzero Pole |
| url | http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-28T07%3A37%3A17IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20the%20Coefficients%20of%20Certain%20Subclasses%20of%20Harmonic%20Univalent%20Mappings%20with%20Nonzero%20Pole&rft.jtitle=Boletim%20da%20Sociedade%20Brasileira%20de%20Matem%C3%A1tica&rft.au=Bhowmik,%20Bappaditya&rft.date=2021-12-01&rft.volume=52&rft.issue=4&rft.spage=1041&rft.epage=1053&rft.pages=1041-1053&rft.issn=1678-7544&rft.eissn=1678-7714&rft_id=info:doi/10.1007/s00574-021-00244-x&rft_dat=%3Cproquest_cross%3E2582804863%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c319t-3e2f8197d2557ca87b2a496a6e6eb8e25527eb8d8aa00d080811a2bd06cb428d3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2582804863&rft_id=info:pmid/&rfr_iscdi=true |