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On certain analytic functions with bounded radius rotation
Certain classes R k ( μ , α ) ; k ≥ 2 , μ > − 1 , 0 ≤ α < 1 of analytic functions are defined in the unit disc using convolution technique. It is shown that functions in R k ( μ , α ) are of bounded radius rotation. It is proved that R k ( μ , α ) and some other newly introduced related classe...
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| Published in: | Computers & mathematics with applications (1987) 2011-05, Vol.61 (10), p.2987-2993 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Subjects: | |
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| Online Access: | Get full text |
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| cited_by | cdi_FETCH-LOGICAL-c335t-2798c962a51cde831b940ed5074e530bf65226ea551ae262eb05bfcbd33f94d13 |
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| cites | cdi_FETCH-LOGICAL-c335t-2798c962a51cde831b940ed5074e530bf65226ea551ae262eb05bfcbd33f94d13 |
| container_end_page | 2993 |
| container_issue | 10 |
| container_start_page | 2987 |
| container_title | Computers & mathematics with applications (1987) |
| container_volume | 61 |
| creator | Noor, Khalida Inayat Noor, Muhammad Aslam Al-Said, Eisa A. |
| description | Certain classes
R
k
(
μ
,
α
)
;
k
≥
2
,
μ
>
−
1
,
0
≤
α
<
1
of analytic functions are defined in the unit disc using convolution technique. It is shown that functions in
R
k
(
μ
,
α
)
are of bounded radius rotation. It is proved that
R
k
(
μ
,
α
)
and some other newly introduced related classes are invariant under the generalized Bernardi integral operator. The converse case as a radius problem is also considered. Theorems proved in this paper are best possible in some sense. |
| doi_str_mv | 10.1016/j.camwa.2011.03.084 |
| format | article |
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R
k
(
μ
,
α
)
;
k
≥
2
,
μ
>
−
1
,
0
≤
α
<
1
of analytic functions are defined in the unit disc using convolution technique. It is shown that functions in
R
k
(
μ
,
α
)
are of bounded radius rotation. It is proved that
R
k
(
μ
,
α
)
and some other newly introduced related classes are invariant under the generalized Bernardi integral operator. The converse case as a radius problem is also considered. Theorems proved in this paper are best possible in some sense.</description><identifier>ISSN: 0898-1221</identifier><identifier>EISSN: 1873-7668</identifier><identifier>DOI: 10.1016/j.camwa.2011.03.084</identifier><language>eng</language><publisher>Elsevier Ltd</publisher><subject>Analytic functions ; Bounded radius rotation ; Convolution ; Discs ; Disks ; Functions with positive real part ; Integrals ; Invariants ; Linear operator ; Mathematical analysis ; Mathematical models ; Operators ; Ruscheweyh derivative ; Starlike</subject><ispartof>Computers & mathematics with applications (1987), 2011-05, Vol.61 (10), p.2987-2993</ispartof><rights>2011 Elsevier Ltd</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c335t-2798c962a51cde831b940ed5074e530bf65226ea551ae262eb05bfcbd33f94d13</citedby><cites>FETCH-LOGICAL-c335t-2798c962a51cde831b940ed5074e530bf65226ea551ae262eb05bfcbd33f94d13</cites></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>Noor, Khalida Inayat</creatorcontrib><creatorcontrib>Noor, Muhammad Aslam</creatorcontrib><creatorcontrib>Al-Said, Eisa A.</creatorcontrib><title>On certain analytic functions with bounded radius rotation</title><title>Computers & mathematics with applications (1987)</title><description>Certain classes
R
k
(
μ
,
α
)
;
k
≥
2
,
μ
>
−
1
,
0
≤
α
<
1
of analytic functions are defined in the unit disc using convolution technique. It is shown that functions in
R
k
(
μ
,
α
)
are of bounded radius rotation. It is proved that
R
k
(
μ
,
α
)
and some other newly introduced related classes are invariant under the generalized Bernardi integral operator. The converse case as a radius problem is also considered. Theorems proved in this paper are best possible in some sense.</description><subject>Analytic functions</subject><subject>Bounded radius rotation</subject><subject>Convolution</subject><subject>Discs</subject><subject>Disks</subject><subject>Functions with positive real part</subject><subject>Integrals</subject><subject>Invariants</subject><subject>Linear operator</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Operators</subject><subject>Ruscheweyh derivative</subject><subject>Starlike</subject><issn>0898-1221</issn><issn>1873-7668</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9kD1PwzAURS0EEqXwC1iyMSU827HjIDGgii-pUheYLcd-Ea5Sp9gOFf-eljIz3eHd86R7CLmmUFGg8nZdWbPZmYoBpRXwClR9QmZUNbxspFSnZAaqVSVljJ6Ti5TWAFBzBjNytwqFxZiND4UJZvjO3hb9FGz2Y0jFzuePohun4NAV0Tg_pSKO2Ryul-SsN0PCq7-ck_enx7fFS7lcPb8uHpal5VzkkjWtsq1kRlDrUHHatTWgE9DUKDh0vRSMSTRCUINMMuxAdL3tHOd9WzvK5-Tm-Hcbx88JU9YbnywOgwk4Tkkr1XIlpDw0-bFp45hSxF5vo9-Y-K0p6IMovda_ovRBlAau96L21P2Rwv2IL49RJ-sxWHQ-os3ajf5f_gcUonJR</recordid><startdate>20110501</startdate><enddate>20110501</enddate><creator>Noor, Khalida Inayat</creator><creator>Noor, Muhammad Aslam</creator><creator>Al-Said, Eisa A.</creator><general>Elsevier Ltd</general><scope>6I.</scope><scope>AAFTH</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20110501</creationdate><title>On certain analytic functions with bounded radius rotation</title><author>Noor, Khalida Inayat ; Noor, Muhammad Aslam ; Al-Said, Eisa A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c335t-2798c962a51cde831b940ed5074e530bf65226ea551ae262eb05bfcbd33f94d13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Analytic functions</topic><topic>Bounded radius rotation</topic><topic>Convolution</topic><topic>Discs</topic><topic>Disks</topic><topic>Functions with positive real part</topic><topic>Integrals</topic><topic>Invariants</topic><topic>Linear operator</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Operators</topic><topic>Ruscheweyh derivative</topic><topic>Starlike</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Noor, Khalida Inayat</creatorcontrib><creatorcontrib>Noor, Muhammad Aslam</creatorcontrib><creatorcontrib>Al-Said, Eisa A.</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Computers & mathematics with applications (1987)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Noor, Khalida Inayat</au><au>Noor, Muhammad Aslam</au><au>Al-Said, Eisa A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On certain analytic functions with bounded radius rotation</atitle><jtitle>Computers & mathematics with applications (1987)</jtitle><date>2011-05-01</date><risdate>2011</risdate><volume>61</volume><issue>10</issue><spage>2987</spage><epage>2993</epage><pages>2987-2993</pages><issn>0898-1221</issn><eissn>1873-7668</eissn><abstract>Certain classes
R
k
(
μ
,
α
)
;
k
≥
2
,
μ
>
−
1
,
0
≤
α
<
1
of analytic functions are defined in the unit disc using convolution technique. It is shown that functions in
R
k
(
μ
,
α
)
are of bounded radius rotation. It is proved that
R
k
(
μ
,
α
)
and some other newly introduced related classes are invariant under the generalized Bernardi integral operator. The converse case as a radius problem is also considered. Theorems proved in this paper are best possible in some sense.</abstract><pub>Elsevier Ltd</pub><doi>10.1016/j.camwa.2011.03.084</doi><tpages>7</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0898-1221 |
| ispartof | Computers & mathematics with applications (1987), 2011-05, Vol.61 (10), p.2987-2993 |
| issn | 0898-1221 1873-7668 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_889385661 |
| source | ScienceDirect Freedom Collection 2022-2024 |
| subjects | Analytic functions Bounded radius rotation Convolution Discs Disks Functions with positive real part Integrals Invariants Linear operator Mathematical analysis Mathematical models Operators Ruscheweyh derivative Starlike |
| title | On certain analytic functions with bounded radius rotation |
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