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Volterra-Type Operators on the Subclasses of Univalent Functions
We examine necessary and sufficient conditions for a member to belong to the class of starlike and convex functions of complex order b ( b ≠ 0) and spirallike functions of type λ − π 2 < λ < π 2 order b ( b ≠ 0) . We obtain sharp estimates for the coefficient of the second term in the Tayl...
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| Published in: | Ukrainian mathematical journal 2022-06, Vol.74 (1), p.87-101 |
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| Language: | English |
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| container_end_page | 101 |
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| container_title | Ukrainian mathematical journal |
| container_volume | 74 |
| creator | Mahboobi, M. |
| description | We examine necessary and sufficient conditions for a member to belong to the class of starlike and convex functions of complex order
b
(
b
≠ 0) and spirallike functions of type
λ
−
π
2
<
λ
<
π
2
order
b
(
b
≠ 0)
.
We obtain sharp estimates for the coefficient of the second term in the Taylor series of functions that belong to the indicated classes. In the main part of the paper, we obtain necessary and sufficient conditions of boundedness for the image of the open unit disk
D
z
∈
ℂ
:
z
<
1
under the action of a Volterra-type operator and the product of a composition operator and a Volterra-type operator in the space of univalent functions and its subspace. Finally, we obtain an estimate for the Schwartzian norm of the above operators in these spaces. |
| doi_str_mv | 10.1007/s11253-022-02049-7 |
| format | article |
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b
(
b
≠ 0) and spirallike functions of type
λ
−
π
2
<
λ
<
π
2
order
b
(
b
≠ 0)
.
We obtain sharp estimates for the coefficient of the second term in the Taylor series of functions that belong to the indicated classes. In the main part of the paper, we obtain necessary and sufficient conditions of boundedness for the image of the open unit disk
D
z
∈
ℂ
:
z
<
1
under the action of a Volterra-type operator and the product of a composition operator and a Volterra-type operator in the space of univalent functions and its subspace. Finally, we obtain an estimate for the Schwartzian norm of the above operators in these spaces.</description><identifier>ISSN: 0041-5995</identifier><identifier>EISSN: 1573-9376</identifier><identifier>DOI: 10.1007/s11253-022-02049-7</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Analysis ; Applications of Mathematics ; Geometry ; Mathematics ; Mathematics and Statistics ; Operators ; Statistics ; Taylor series</subject><ispartof>Ukrainian mathematical journal, 2022-06, Vol.74 (1), p.87-101</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><rights>COPYRIGHT 2022 Springer</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c239t-f92aa15e8460288833e09649370a380c40d6a787a71c3805f6c5ce3420f939f73</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,777,781,27905,27906</link.rule.ids></links><search><creatorcontrib>Mahboobi, M.</creatorcontrib><title>Volterra-Type Operators on the Subclasses of Univalent Functions</title><title>Ukrainian mathematical journal</title><addtitle>Ukr Math J</addtitle><description>We examine necessary and sufficient conditions for a member to belong to the class of starlike and convex functions of complex order
b
(
b
≠ 0) and spirallike functions of type
λ
−
π
2
<
λ
<
π
2
order
b
(
b
≠ 0)
.
We obtain sharp estimates for the coefficient of the second term in the Taylor series of functions that belong to the indicated classes. In the main part of the paper, we obtain necessary and sufficient conditions of boundedness for the image of the open unit disk
D
z
∈
ℂ
:
z
<
1
under the action of a Volterra-type operator and the product of a composition operator and a Volterra-type operator in the space of univalent functions and its subspace. Finally, we obtain an estimate for the Schwartzian norm of the above operators in these spaces.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Geometry</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operators</subject><subject>Statistics</subject><subject>Taylor series</subject><issn>0041-5995</issn><issn>1573-9376</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kM1KAzEURoMoWKsv4GrA9dSbn5kkO0uxKhS6sHUbYprUKdNkTKZC397UEdxJCCGX7yQfB6FbDBMMwO8TxqSiJRCSNzBZ8jM0whWnpaS8PkcjAIbLSsrqEl2ltAPImOAj9PAW2t7GqMvVsbPFsrNR9yGmIvii_7DF6-HdtDolmyeuWPvmS7fW98X84E3fBJ-u0YXTbbI3v-cYreePq9lzuVg-vcymi9IQKvvSSaI1rqxgNRAhBKUWZM1yO9BUgGGwqTUXXHNs8r1ytamMpYyAk1Q6Tsfobni3i-HzYFOvduEQff5SEU6oYJQBy6nJkNrmmqrxLvRRm7w2dt-Y4K1r8nzKCSOizmYyQAbAxJBStE51sdnreFQY1EmtGtSqrFb9qFWnLnSAUg77rY1_Xf6hvgF3oXmf</recordid><startdate>20220601</startdate><enddate>20220601</enddate><creator>Mahboobi, M.</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20220601</creationdate><title>Volterra-Type Operators on the Subclasses of Univalent Functions</title><author>Mahboobi, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c239t-f92aa15e8460288833e09649370a380c40d6a787a71c3805f6c5ce3420f939f73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Geometry</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operators</topic><topic>Statistics</topic><topic>Taylor series</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mahboobi, M.</creatorcontrib><collection>CrossRef</collection><jtitle>Ukrainian mathematical journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mahboobi, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Volterra-Type Operators on the Subclasses of Univalent Functions</atitle><jtitle>Ukrainian mathematical journal</jtitle><stitle>Ukr Math J</stitle><date>2022-06-01</date><risdate>2022</risdate><volume>74</volume><issue>1</issue><spage>87</spage><epage>101</epage><pages>87-101</pages><issn>0041-5995</issn><eissn>1573-9376</eissn><abstract>We examine necessary and sufficient conditions for a member to belong to the class of starlike and convex functions of complex order
b
(
b
≠ 0) and spirallike functions of type
λ
−
π
2
<
λ
<
π
2
order
b
(
b
≠ 0)
.
We obtain sharp estimates for the coefficient of the second term in the Taylor series of functions that belong to the indicated classes. In the main part of the paper, we obtain necessary and sufficient conditions of boundedness for the image of the open unit disk
D
z
∈
ℂ
:
z
<
1
under the action of a Volterra-type operator and the product of a composition operator and a Volterra-type operator in the space of univalent functions and its subspace. Finally, we obtain an estimate for the Schwartzian norm of the above operators in these spaces.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11253-022-02049-7</doi><tpages>15</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0041-5995 |
| ispartof | Ukrainian mathematical journal, 2022-06, Vol.74 (1), p.87-101 |
| issn | 0041-5995 1573-9376 |
| language | eng |
| recordid | cdi_proquest_journals_2723843404 |
| source | Springer Link |
| subjects | Algebra Analysis Applications of Mathematics Geometry Mathematics Mathematics and Statistics Operators Statistics Taylor series |
| title | Volterra-Type Operators on the Subclasses of Univalent Functions |
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