On an Operator Preserving Inequalities Between Polynomials
Let P ( z ) be a polynomial of degree n. We consider an operator D α that maps P ( z ) into D α P ( z ) := nP ( z ) + (α − z ) P0 ( z ) and establish some results concerning the estimates of |D α P ( z ) | in the disk |z| = R ≥ 1 , and thereby obtain extensions and generalizations of numerous well-k...
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| Veröffentlicht in: | Ukrainian mathematical journal 2018, Vol.69 (8), p.1234-1247 |
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| container_title | Ukrainian mathematical journal |
| container_volume | 69 |
| creator | Mir, A. |
| description | Let
P
(
z
) be a polynomial of degree
n.
We consider an operator
D
α
that maps
P
(
z
) into
D
α
P
(
z
) :=
nP
(
z
) + (α
− z
)
P0
(
z
) and establish some results concerning the estimates of
|D
α
P
(
z
)
|
in the disk
|z|
=
R ≥
1
,
and thereby obtain extensions and generalizations of numerous well-known inequalities for polynomial. |
| doi_str_mv | 10.1007/s11253-017-1427-2 |
| format | Article |
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P
(
z
) be a polynomial of degree
n.
We consider an operator
D
α
that maps
P
(
z
) into
D
α
P
(
z
) :=
nP
(
z
) + (α
− z
)
P0
(
z
) and establish some results concerning the estimates of
|D
α
P
(
z
)
|
in the disk
|z|
=
R ≥
1
,
and thereby obtain extensions and generalizations of numerous well-known inequalities for polynomial.</description><identifier>ISSN: 0041-5995</identifier><identifier>EISSN: 1573-9376</identifier><identifier>DOI: 10.1007/s11253-017-1427-2</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Analysis ; Applications of Mathematics ; Geometry ; Inequalities ; Mathematics ; Mathematics and Statistics ; Polynomials ; Statistics</subject><ispartof>Ukrainian mathematical journal, 2018, Vol.69 (8), p.1234-1247</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2017</rights><rights>COPYRIGHT 2018 Springer</rights><rights>Copyright Springer Science & Business Media 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-95df9a0ba0f2d415f6a86d094c8082a9ed942b07c6e49816c1897001243ed6d03</citedby><cites>FETCH-LOGICAL-c355t-95df9a0ba0f2d415f6a86d094c8082a9ed942b07c6e49816c1897001243ed6d03</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11253-017-1427-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11253-017-1427-2$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Mir, A.</creatorcontrib><title>On an Operator Preserving Inequalities Between Polynomials</title><title>Ukrainian mathematical journal</title><addtitle>Ukr Math J</addtitle><description>Let
P
(
z
) be a polynomial of degree
n.
We consider an operator
D
α
that maps
P
(
z
) into
D
α
P
(
z
) :=
nP
(
z
) + (α
− z
)
P0
(
z
) and establish some results concerning the estimates of
|D
α
P
(
z
)
|
in the disk
|z|
=
R ≥
1
,
and thereby obtain extensions and generalizations of numerous well-known inequalities for polynomial.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Geometry</subject><subject>Inequalities</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Polynomials</subject><subject>Statistics</subject><issn>0041-5995</issn><issn>1573-9376</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kM1LAzEQxYMoWKt_gLcFz6mZbD423mrxo1BoD3oO6e5s2bLNtslW6X9vynrwInN4MLzfzOMRcg9sAozpxwjAZU4ZaAqCa8ovyAikzqnJtbokI8YEUGmMvCY3MW4ZS1ShR-Rp6TPns-Ueg-u7kK0CRgxfjd9kc4-Ho2ubvsGYPWP_jeizVdeefLdrXBtvyVWdBO9-dUw-X18-Zu90sXybz6YLWuZS9tTIqjaOrR2reSVA1soVqmJGlAUruDNYGcHXTJcKhSlAlVAYnfJxkWOVjPmYPAx396E7HDH2dtsdg08vLRidS6ZAieSaDK6Na9E2vu764Mo0Fe6asvNYN2k_lVwBKGNUAmAAytDFGLC2-9DsXDhZYPbcqR06talTe-7U8sTwgYnJ6zcY_kT5F_oBg6N3ig</recordid><startdate>2018</startdate><enddate>2018</enddate><creator>Mir, A.</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>2018</creationdate><title>On an Operator Preserving Inequalities Between Polynomials</title><author>Mir, A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-95df9a0ba0f2d415f6a86d094c8082a9ed942b07c6e49816c1897001243ed6d03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Geometry</topic><topic>Inequalities</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Polynomials</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mir, A.</creatorcontrib><collection>CrossRef</collection><jtitle>Ukrainian mathematical journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mir, A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On an Operator Preserving Inequalities Between Polynomials</atitle><jtitle>Ukrainian mathematical journal</jtitle><stitle>Ukr Math J</stitle><date>2018</date><risdate>2018</risdate><volume>69</volume><issue>8</issue><spage>1234</spage><epage>1247</epage><pages>1234-1247</pages><issn>0041-5995</issn><eissn>1573-9376</eissn><abstract>Let
P
(
z
) be a polynomial of degree
n.
We consider an operator
D
α
that maps
P
(
z
) into
D
α
P
(
z
) :=
nP
(
z
) + (α
− z
)
P0
(
z
) and establish some results concerning the estimates of
|D
α
P
(
z
)
|
in the disk
|z|
=
R ≥
1
,
and thereby obtain extensions and generalizations of numerous well-known inequalities for polynomial.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11253-017-1427-2</doi><tpages>14</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0041-5995 |
| ispartof | Ukrainian mathematical journal, 2018, Vol.69 (8), p.1234-1247 |
| issn | 0041-5995 1573-9376 |
| language | eng |
| recordid | cdi_proquest_journals_1973506164 |
| source | SpringerLink Journals |
| subjects | Algebra Analysis Applications of Mathematics Geometry Inequalities Mathematics Mathematics and Statistics Polynomials Statistics |
| title | On an Operator Preserving Inequalities Between Polynomials |
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