On restricted functional inequalities associated with quadratic functional equations
In this paper it is proved that, for a function f : X → E mapping from a normed linear space X into an inner product space E , the functional inequality ‖ 2 f ( x ) + 2 f ( y ) - f ( x - y ) ‖ ⩽ ‖ f ( x + y ) ‖ , ‖ x ‖ + ‖ y ‖ ⩾ d for some d > 0 , implies f is quadratic. Other types of functional...
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Veröffentlicht in: | Aequationes mathematicae 2022, Vol.96 (4), p.763-772 |
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description | In this paper it is proved that, for a function
f
:
X
→
E
mapping from a normed linear space
X
into an inner product space
E
, the functional inequality
‖
2
f
(
x
)
+
2
f
(
y
)
-
f
(
x
-
y
)
‖
⩽
‖
f
(
x
+
y
)
‖
,
‖
x
‖
+
‖
y
‖
⩾
d
for some
d
>
0
, implies
f
is quadratic. Other types of functional inequalities related to the quadratic functional equation have also been investigated. Besides we establish the Hyers–Ulam stability on restricted domains, and we improve the bounds and thus the stability results obtained in Jung (J Math Anal Appl 222:126–137, 1998) and Rassias (J Math Anal Appl 276: 747–762, 2002). Finally we apply our recent results to the asymptotic behavior of quadratic functional equations of different types. |
doi_str_mv | 10.1007/s00010-022-00872-8 |
format | Article |
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f
:
X
→
E
mapping from a normed linear space
X
into an inner product space
E
, the functional inequality
‖
2
f
(
x
)
+
2
f
(
y
)
-
f
(
x
-
y
)
‖
⩽
‖
f
(
x
+
y
)
‖
,
‖
x
‖
+
‖
y
‖
⩾
d
for some
d
>
0
, implies
f
is quadratic. Other types of functional inequalities related to the quadratic functional equation have also been investigated. Besides we establish the Hyers–Ulam stability on restricted domains, and we improve the bounds and thus the stability results obtained in Jung (J Math Anal Appl 222:126–137, 1998) and Rassias (J Math Anal Appl 276: 747–762, 2002). Finally we apply our recent results to the asymptotic behavior of quadratic functional equations of different types.</description><identifier>ISSN: 0001-9054</identifier><identifier>EISSN: 1420-8903</identifier><identifier>DOI: 10.1007/s00010-022-00872-8</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Asymptotic properties ; Combinatorics ; Functional equations ; Inequalities ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Quadratic equations ; Stability</subject><ispartof>Aequationes mathematicae, 2022, Vol.96 (4), p.763-772</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022</rights><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-cf88cac107c1d0ab86dfcdaa81689973d8e780f496cb0fa201209b6400bbaaa53</citedby><cites>FETCH-LOGICAL-c319t-cf88cac107c1d0ab86dfcdaa81689973d8e780f496cb0fa201209b6400bbaaa53</cites><orcidid>0000-0001-7563-0507</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00010-022-00872-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00010-022-00872-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Tareeghee, M. A.</creatorcontrib><creatorcontrib>Najati, A.</creatorcontrib><creatorcontrib>Abdollahpour, M. R.</creatorcontrib><creatorcontrib>Noori, B.</creatorcontrib><title>On restricted functional inequalities associated with quadratic functional equations</title><title>Aequationes mathematicae</title><addtitle>Aequat. Math</addtitle><description>In this paper it is proved that, for a function
f
:
X
→
E
mapping from a normed linear space
X
into an inner product space
E
, the functional inequality
‖
2
f
(
x
)
+
2
f
(
y
)
-
f
(
x
-
y
)
‖
⩽
‖
f
(
x
+
y
)
‖
,
‖
x
‖
+
‖
y
‖
⩾
d
for some
d
>
0
, implies
f
is quadratic. Other types of functional inequalities related to the quadratic functional equation have also been investigated. Besides we establish the Hyers–Ulam stability on restricted domains, and we improve the bounds and thus the stability results obtained in Jung (J Math Anal Appl 222:126–137, 1998) and Rassias (J Math Anal Appl 276: 747–762, 2002). Finally we apply our recent results to the asymptotic behavior of quadratic functional equations of different types.</description><subject>Analysis</subject><subject>Asymptotic properties</subject><subject>Combinatorics</subject><subject>Functional equations</subject><subject>Inequalities</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Quadratic equations</subject><subject>Stability</subject><issn>0001-9054</issn><issn>1420-8903</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kEFLAzEQhYMoWKt_wNOC5-gku90kRylqhUIv9Rxms4mm1N02ySL-e7OuoCdPM8N87zHzCLlmcMsAxF0EAAYUOKcAUnAqT8iMVRyoVFCektm4pwoW1Tm5iHGXJy5EOSPbTVcEG1PwJtm2cENnku873Be-s8cB9z55GwuMsTceR-TDp7cib9qAyZu_ipEf23hJzhzuo736qXPy8viwXa7oevP0vLxfU1MylahxUho0DIRhLWAj69aZFlGyWiolylZaIcFVqjYNOOT5ZlBNXQE0DSIuyjm5mXwPoT8O-Qu964eQT4maZwu2qBSvMsUnyoQ-xmCdPgT_juFTM9BjenpKT-f09Hd6WmZROYlihrtXG36t_1F9ARYbdEc</recordid><startdate>2022</startdate><enddate>2022</enddate><creator>Tareeghee, M. A.</creator><creator>Najati, A.</creator><creator>Abdollahpour, M. R.</creator><creator>Noori, B.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0001-7563-0507</orcidid></search><sort><creationdate>2022</creationdate><title>On restricted functional inequalities associated with quadratic functional equations</title><author>Tareeghee, M. A. ; Najati, A. ; Abdollahpour, M. R. ; Noori, B.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-cf88cac107c1d0ab86dfcdaa81689973d8e780f496cb0fa201209b6400bbaaa53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Analysis</topic><topic>Asymptotic properties</topic><topic>Combinatorics</topic><topic>Functional equations</topic><topic>Inequalities</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Quadratic equations</topic><topic>Stability</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Tareeghee, M. A.</creatorcontrib><creatorcontrib>Najati, A.</creatorcontrib><creatorcontrib>Abdollahpour, M. R.</creatorcontrib><creatorcontrib>Noori, B.</creatorcontrib><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>Aerospace 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>Aequationes mathematicae</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Tareeghee, M. A.</au><au>Najati, A.</au><au>Abdollahpour, M. R.</au><au>Noori, B.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On restricted functional inequalities associated with quadratic functional equations</atitle><jtitle>Aequationes mathematicae</jtitle><stitle>Aequat. Math</stitle><date>2022</date><risdate>2022</risdate><volume>96</volume><issue>4</issue><spage>763</spage><epage>772</epage><pages>763-772</pages><issn>0001-9054</issn><eissn>1420-8903</eissn><abstract>In this paper it is proved that, for a function
f
:
X
→
E
mapping from a normed linear space
X
into an inner product space
E
, the functional inequality
‖
2
f
(
x
)
+
2
f
(
y
)
-
f
(
x
-
y
)
‖
⩽
‖
f
(
x
+
y
)
‖
,
‖
x
‖
+
‖
y
‖
⩾
d
for some
d
>
0
, implies
f
is quadratic. Other types of functional inequalities related to the quadratic functional equation have also been investigated. Besides we establish the Hyers–Ulam stability on restricted domains, and we improve the bounds and thus the stability results obtained in Jung (J Math Anal Appl 222:126–137, 1998) and Rassias (J Math Anal Appl 276: 747–762, 2002). Finally we apply our recent results to the asymptotic behavior of quadratic functional equations of different types.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00010-022-00872-8</doi><tpages>10</tpages><orcidid>https://orcid.org/0000-0001-7563-0507</orcidid></addata></record> |
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subjects | Analysis Asymptotic properties Combinatorics Functional equations Inequalities Mathematical analysis Mathematics Mathematics and Statistics Quadratic equations Stability |
title | On restricted functional inequalities associated with quadratic functional equations |
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