Minkowski-type inequalities involving Hardy function and symmetric functions
The Hardy matrix H n ( x , α ) , the Hardy function per H n ( x , α ) and the generalized Vandermonde determinant det H n ( x , α ) are defined in this paper. By means of algebra and analysis theories together with proper hypotheses, we establish the following Minkowski-type inequality involving Har...
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| Veröffentlicht in: | Journal of inequalities and applications 2014-05, Vol.2014 (1), p.1-17, Article 186 |
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| container_title | Journal of inequalities and applications |
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| creator | Wen, JiaJin Wu, ShanHe Han, TianYong |
| description | The Hardy matrix
H
n
(
x
,
α
)
, the Hardy function
per
H
n
(
x
,
α
)
and the generalized Vandermonde determinant
det
H
n
(
x
,
α
)
are defined in this paper. By means of algebra and analysis theories together with proper hypotheses, we establish the following Minkowski-type inequality involving Hardy function:
[
per
H
n
(
x
+
y
,
α
)
]
1
|
α
|
⩾
[
per
H
n
(
x
,
α
)
]
1
|
α
|
+
[
per
H
n
(
y
,
α
)
]
1
|
α
|
.
As applications, our inequality is used to estimate the lower bounds of the increment of a symmetric function.
MSC:
26D15, 15A15. |
| doi_str_mv | 10.1186/1029-242X-2014-186 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1718963195</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1718963195</sourcerecordid><originalsourceid>FETCH-LOGICAL-c396t-dd9f6cd543689f5fcd5e79155700adcd2f5137268c501f25eb460dba68a9c9fe3</originalsourceid><addsrcrecordid>eNp1kEtLAzEUhYMoWB9_wNWAGzejSWaSSZZS1AoVNwruQppHSTuTaZOZyvx7M1RKEVzdcw_fuVwOADcI3iPE6AOCmOe4xF85hqjMk3UCJgfz9Eifg4sYVxBiVLByAuZvzq_b77h2eTdsTOa82faydp0zMS27tt45v8xmMughs71XnWt9Jr3O4tA0pgtOHex4Bc6srKO5_p2X4PP56WM6y-fvL6_Tx3muCk67XGtuqdKkLCjjltgkTcURIRWEUiuNLUFFhSlTBCKLiVmUFOqFpExyxa0pLsHd_u4mtNvexE40LipT19Kbto8CVYhxWiBOEnr7B121ffDpO4Eog7zkmKJE4T2lQhtjMFZsgmtkGASCYixYjP2JsT8xFiySlULFPhQT7JcmHJ3-P_UDmpB-4A</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1680949261</pqid></control><display><type>article</type><title>Minkowski-type inequalities involving Hardy function and symmetric functions</title><source>DOAJ Directory of Open Access Journals</source><source>Springer Nature OA Free Journals</source><source>EZB-FREE-00999 freely available EZB journals</source><source>SpringerLink Journals - AutoHoldings</source><creator>Wen, JiaJin ; Wu, ShanHe ; Han, TianYong</creator><creatorcontrib>Wen, JiaJin ; Wu, ShanHe ; Han, TianYong</creatorcontrib><description>The Hardy matrix
H
n
(
x
,
α
)
, the Hardy function
per
H
n
(
x
,
α
)
and the generalized Vandermonde determinant
det
H
n
(
x
,
α
)
are defined in this paper. By means of algebra and analysis theories together with proper hypotheses, we establish the following Minkowski-type inequality involving Hardy function:
[
per
H
n
(
x
+
y
,
α
)
]
1
|
α
|
⩾
[
per
H
n
(
x
,
α
)
]
1
|
α
|
+
[
per
H
n
(
y
,
α
)
]
1
|
α
|
.
As applications, our inequality is used to estimate the lower bounds of the increment of a symmetric function.
MSC:
26D15, 15A15.</description><identifier>ISSN: 1029-242X</identifier><identifier>ISSN: 1025-5834</identifier><identifier>EISSN: 1029-242X</identifier><identifier>DOI: 10.1186/1029-242X-2014-186</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Algebra ; Analysis ; Applications of Mathematics ; Determinants ; Estimates ; Hypotheses ; Inequalities ; Lower bounds ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Symmetry</subject><ispartof>Journal of inequalities and applications, 2014-05, Vol.2014 (1), p.1-17, Article 186</ispartof><rights>Wen et al.; licensee Springer. 2014. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.</rights><rights>The Author(s) 2014</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c396t-dd9f6cd543689f5fcd5e79155700adcd2f5137268c501f25eb460dba68a9c9fe3</citedby><cites>FETCH-LOGICAL-c396t-dd9f6cd543689f5fcd5e79155700adcd2f5137268c501f25eb460dba68a9c9fe3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1186/1029-242X-2014-186$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1186/1029-242X-2014-186$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,777,781,861,27905,27906,41101,41469,42170,42538,51300,51557</link.rule.ids></links><search><creatorcontrib>Wen, JiaJin</creatorcontrib><creatorcontrib>Wu, ShanHe</creatorcontrib><creatorcontrib>Han, TianYong</creatorcontrib><title>Minkowski-type inequalities involving Hardy function and symmetric functions</title><title>Journal of inequalities and applications</title><addtitle>J Inequal Appl</addtitle><description>The Hardy matrix
H
n
(
x
,
α
)
, the Hardy function
per
H
n
(
x
,
α
)
and the generalized Vandermonde determinant
det
H
n
(
x
,
α
)
are defined in this paper. By means of algebra and analysis theories together with proper hypotheses, we establish the following Minkowski-type inequality involving Hardy function:
[
per
H
n
(
x
+
y
,
α
)
]
1
|
α
|
⩾
[
per
H
n
(
x
,
α
)
]
1
|
α
|
+
[
per
H
n
(
y
,
α
)
]
1
|
α
|
.
As applications, our inequality is used to estimate the lower bounds of the increment of a symmetric function.
MSC:
26D15, 15A15.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Determinants</subject><subject>Estimates</subject><subject>Hypotheses</subject><subject>Inequalities</subject><subject>Lower bounds</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Symmetry</subject><issn>1029-242X</issn><issn>1025-5834</issn><issn>1029-242X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp1kEtLAzEUhYMoWB9_wNWAGzejSWaSSZZS1AoVNwruQppHSTuTaZOZyvx7M1RKEVzdcw_fuVwOADcI3iPE6AOCmOe4xF85hqjMk3UCJgfz9Eifg4sYVxBiVLByAuZvzq_b77h2eTdsTOa82faydp0zMS27tt45v8xmMughs71XnWt9Jr3O4tA0pgtOHex4Bc6srKO5_p2X4PP56WM6y-fvL6_Tx3muCk67XGtuqdKkLCjjltgkTcURIRWEUiuNLUFFhSlTBCKLiVmUFOqFpExyxa0pLsHd_u4mtNvexE40LipT19Kbto8CVYhxWiBOEnr7B121ffDpO4Eog7zkmKJE4T2lQhtjMFZsgmtkGASCYixYjP2JsT8xFiySlULFPhQT7JcmHJ3-P_UDmpB-4A</recordid><startdate>20140513</startdate><enddate>20140513</enddate><creator>Wen, JiaJin</creator><creator>Wu, ShanHe</creator><creator>Han, TianYong</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20140513</creationdate><title>Minkowski-type inequalities involving Hardy function and symmetric functions</title><author>Wen, JiaJin ; Wu, ShanHe ; Han, TianYong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c396t-dd9f6cd543689f5fcd5e79155700adcd2f5137268c501f25eb460dba68a9c9fe3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Determinants</topic><topic>Estimates</topic><topic>Hypotheses</topic><topic>Inequalities</topic><topic>Lower bounds</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Symmetry</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wen, JiaJin</creatorcontrib><creatorcontrib>Wu, ShanHe</creatorcontrib><creatorcontrib>Han, TianYong</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><jtitle>Journal of inequalities and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wen, JiaJin</au><au>Wu, ShanHe</au><au>Han, TianYong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Minkowski-type inequalities involving Hardy function and symmetric functions</atitle><jtitle>Journal of inequalities and applications</jtitle><stitle>J Inequal Appl</stitle><date>2014-05-13</date><risdate>2014</risdate><volume>2014</volume><issue>1</issue><spage>1</spage><epage>17</epage><pages>1-17</pages><artnum>186</artnum><issn>1029-242X</issn><issn>1025-5834</issn><eissn>1029-242X</eissn><abstract>The Hardy matrix
H
n
(
x
,
α
)
, the Hardy function
per
H
n
(
x
,
α
)
and the generalized Vandermonde determinant
det
H
n
(
x
,
α
)
are defined in this paper. By means of algebra and analysis theories together with proper hypotheses, we establish the following Minkowski-type inequality involving Hardy function:
[
per
H
n
(
x
+
y
,
α
)
]
1
|
α
|
⩾
[
per
H
n
(
x
,
α
)
]
1
|
α
|
+
[
per
H
n
(
y
,
α
)
]
1
|
α
|
.
As applications, our inequality is used to estimate the lower bounds of the increment of a symmetric function.
MSC:
26D15, 15A15.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1186/1029-242X-2014-186</doi><tpages>17</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1029-242X |
| ispartof | Journal of inequalities and applications, 2014-05, Vol.2014 (1), p.1-17, Article 186 |
| issn | 1029-242X 1025-5834 1029-242X |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1718963195 |
| source | DOAJ Directory of Open Access Journals; Springer Nature OA Free Journals; EZB-FREE-00999 freely available EZB journals; SpringerLink Journals - AutoHoldings |
| subjects | Algebra Analysis Applications of Mathematics Determinants Estimates Hypotheses Inequalities Lower bounds Mathematical analysis Mathematics Mathematics and Statistics Symmetry |
| title | Minkowski-type inequalities involving Hardy function and symmetric functions |
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