The stability of N-dimensional quadratic functional inequality in non Archimedean Banach spaces
In this paper, using the direct method, we study the stability of the following inequality: f ∑ i = 1 n x i + ∑ 1 ≤ i ≺ j ≤ n f ( x i - x j ) - n ∑ i = 1 n f ( x i ) ≤ f ∑ i = 1 n x i n + ∑ 1 ≤ i ≺ j ≤ n f x i - x j n - 1 n ∑ i = 1 n f ( x i ) in Banach spaces, and the stability of the following ine...
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| Veröffentlicht in: | São Paulo Journal of Mathematical Sciences 2022-12, Vol.16 (2), p.1382-1400 |
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| creator | Aribou, Y. Kabbaj, S. |
| description | In this paper, using the direct method, we study the stability of the following inequality:
f
∑
i
=
1
n
x
i
+
∑
1
≤
i
≺
j
≤
n
f
(
x
i
-
x
j
)
-
n
∑
i
=
1
n
f
(
x
i
)
≤
f
∑
i
=
1
n
x
i
n
+
∑
1
≤
i
≺
j
≤
n
f
x
i
-
x
j
n
-
1
n
∑
i
=
1
n
f
(
x
i
)
in Banach spaces, and the stability of the following inequality:
f
∑
i
=
1
n
x
i
n
+
∑
1
≤
i
≺
j
≤
n
f
x
i
-
x
j
n
-
1
n
∑
i
=
1
n
f
(
x
i
)
∗
≤
f
∑
i
=
1
n
x
i
+
∑
1
≤
i
≺
j
≤
n
f
(
x
i
-
x
j
)
-
n
∑
i
=
1
n
f
(
x
i
)
∗
,
in non-Archimedean Banach spaces with
n
an integer greater than or equal to 2. |
| doi_str_mv | 10.1007/s40863-021-00220-9 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2741010262</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2741010262</sourcerecordid><originalsourceid>FETCH-LOGICAL-c270t-9f4d3bdccefefc3588662e925c8e77c20487f19053a3c01e78ed43627df637e63</originalsourceid><addsrcrecordid>eNp9kE1LAzEQhoMoWGr_gKeA5-gk2c3HsRa_oOilnkOaTWxKm22T3UP_vWtX8OZcBob3eRkehG4p3FMA-VAqUIITYJQAMAZEX6AJ41QQDUxdognVihGhQV6jWSlbGKaupK5hgsxq43Hp7DruYnfCbcDvpIl7n0psk93hY2-bbLvocOiT68ZjTH64n4GYcGoTnme3GajG24QfbbJug8vBOl9u0FWwu-Jnv3uKPp-fVotXsvx4eVvMl8QxCR3RoWr4unHOBx8cr5USgnnNaqe8lI5BpWSgGmpuuQPqpfJNxQWTTRBcesGn6G7sPeT22PvSmW3b5-HZYpisKFBggg0pNqZcbkvJPphDjnubT4aC-XFpRpdmcGnOLo0eID5CZQinL5__qv-hvgFoP3c6</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2741010262</pqid></control><display><type>article</type><title>The stability of N-dimensional quadratic functional inequality in non Archimedean Banach spaces</title><source>SpringerLink Journals - AutoHoldings</source><creator>Aribou, Y. ; Kabbaj, S.</creator><creatorcontrib>Aribou, Y. ; Kabbaj, S.</creatorcontrib><description>In this paper, using the direct method, we study the stability of the following inequality:
f
∑
i
=
1
n
x
i
+
∑
1
≤
i
≺
j
≤
n
f
(
x
i
-
x
j
)
-
n
∑
i
=
1
n
f
(
x
i
)
≤
f
∑
i
=
1
n
x
i
n
+
∑
1
≤
i
≺
j
≤
n
f
x
i
-
x
j
n
-
1
n
∑
i
=
1
n
f
(
x
i
)
in Banach spaces, and the stability of the following inequality:
f
∑
i
=
1
n
x
i
n
+
∑
1
≤
i
≺
j
≤
n
f
x
i
-
x
j
n
-
1
n
∑
i
=
1
n
f
(
x
i
)
∗
≤
f
∑
i
=
1
n
x
i
+
∑
1
≤
i
≺
j
≤
n
f
(
x
i
-
x
j
)
-
n
∑
i
=
1
n
f
(
x
i
)
∗
,
in non-Archimedean Banach spaces with
n
an integer greater than or equal to 2.</description><identifier>ISSN: 1982-6907</identifier><identifier>EISSN: 2316-9028</identifier><identifier>EISSN: 2306-9028</identifier><identifier>DOI: 10.1007/s40863-021-00220-9</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Banach spaces ; Dimensional stability ; Mathematics ; Mathematics and Statistics ; Original Article</subject><ispartof>São Paulo Journal of Mathematical Sciences, 2022-12, Vol.16 (2), p.1382-1400</ispartof><rights>Instituto de Matemática e Estatística da Universidade de São Paulo 2021</rights><rights>Instituto de Matemática e Estatística da Universidade de São Paulo 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-9f4d3bdccefefc3588662e925c8e77c20487f19053a3c01e78ed43627df637e63</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/s40863-021-00220-9$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40863-021-00220-9$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Aribou, Y.</creatorcontrib><creatorcontrib>Kabbaj, S.</creatorcontrib><title>The stability of N-dimensional quadratic functional inequality in non Archimedean Banach spaces</title><title>São Paulo Journal of Mathematical Sciences</title><addtitle>São Paulo J. Math. Sci</addtitle><description>In this paper, using the direct method, we study the stability of the following inequality:
f
∑
i
=
1
n
x
i
+
∑
1
≤
i
≺
j
≤
n
f
(
x
i
-
x
j
)
-
n
∑
i
=
1
n
f
(
x
i
)
≤
f
∑
i
=
1
n
x
i
n
+
∑
1
≤
i
≺
j
≤
n
f
x
i
-
x
j
n
-
1
n
∑
i
=
1
n
f
(
x
i
)
in Banach spaces, and the stability of the following inequality:
f
∑
i
=
1
n
x
i
n
+
∑
1
≤
i
≺
j
≤
n
f
x
i
-
x
j
n
-
1
n
∑
i
=
1
n
f
(
x
i
)
∗
≤
f
∑
i
=
1
n
x
i
+
∑
1
≤
i
≺
j
≤
n
f
(
x
i
-
x
j
)
-
n
∑
i
=
1
n
f
(
x
i
)
∗
,
in non-Archimedean Banach spaces with
n
an integer greater than or equal to 2.</description><subject>Banach spaces</subject><subject>Dimensional stability</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Article</subject><issn>1982-6907</issn><issn>2316-9028</issn><issn>2306-9028</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWGr_gKeA5-gk2c3HsRa_oOilnkOaTWxKm22T3UP_vWtX8OZcBob3eRkehG4p3FMA-VAqUIITYJQAMAZEX6AJ41QQDUxdognVihGhQV6jWSlbGKaupK5hgsxq43Hp7DruYnfCbcDvpIl7n0psk93hY2-bbLvocOiT68ZjTH64n4GYcGoTnme3GajG24QfbbJug8vBOl9u0FWwu-Jnv3uKPp-fVotXsvx4eVvMl8QxCR3RoWr4unHOBx8cr5USgnnNaqe8lI5BpWSgGmpuuQPqpfJNxQWTTRBcesGn6G7sPeT22PvSmW3b5-HZYpisKFBggg0pNqZcbkvJPphDjnubT4aC-XFpRpdmcGnOLo0eID5CZQinL5__qv-hvgFoP3c6</recordid><startdate>20221201</startdate><enddate>20221201</enddate><creator>Aribou, Y.</creator><creator>Kabbaj, S.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20221201</creationdate><title>The stability of N-dimensional quadratic functional inequality in non Archimedean Banach spaces</title><author>Aribou, Y. ; Kabbaj, S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-9f4d3bdccefefc3588662e925c8e77c20487f19053a3c01e78ed43627df637e63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Banach spaces</topic><topic>Dimensional stability</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Article</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Aribou, Y.</creatorcontrib><creatorcontrib>Kabbaj, S.</creatorcontrib><collection>CrossRef</collection><jtitle>São Paulo Journal of Mathematical Sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Aribou, Y.</au><au>Kabbaj, S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The stability of N-dimensional quadratic functional inequality in non Archimedean Banach spaces</atitle><jtitle>São Paulo Journal of Mathematical Sciences</jtitle><stitle>São Paulo J. Math. Sci</stitle><date>2022-12-01</date><risdate>2022</risdate><volume>16</volume><issue>2</issue><spage>1382</spage><epage>1400</epage><pages>1382-1400</pages><issn>1982-6907</issn><eissn>2316-9028</eissn><eissn>2306-9028</eissn><abstract>In this paper, using the direct method, we study the stability of the following inequality:
f
∑
i
=
1
n
x
i
+
∑
1
≤
i
≺
j
≤
n
f
(
x
i
-
x
j
)
-
n
∑
i
=
1
n
f
(
x
i
)
≤
f
∑
i
=
1
n
x
i
n
+
∑
1
≤
i
≺
j
≤
n
f
x
i
-
x
j
n
-
1
n
∑
i
=
1
n
f
(
x
i
)
in Banach spaces, and the stability of the following inequality:
f
∑
i
=
1
n
x
i
n
+
∑
1
≤
i
≺
j
≤
n
f
x
i
-
x
j
n
-
1
n
∑
i
=
1
n
f
(
x
i
)
∗
≤
f
∑
i
=
1
n
x
i
+
∑
1
≤
i
≺
j
≤
n
f
(
x
i
-
x
j
)
-
n
∑
i
=
1
n
f
(
x
i
)
∗
,
in non-Archimedean Banach spaces with
n
an integer greater than or equal to 2.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s40863-021-00220-9</doi><tpages>19</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1982-6907 |
| ispartof | São Paulo Journal of Mathematical Sciences, 2022-12, Vol.16 (2), p.1382-1400 |
| issn | 1982-6907 2316-9028 2306-9028 |
| language | eng |
| recordid | cdi_proquest_journals_2741010262 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Banach spaces Dimensional stability Mathematics Mathematics and Statistics Original Article |
| title | The stability of N-dimensional quadratic functional inequality in non Archimedean Banach spaces |
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