A New Variant of Wilson’s Functional Equation on Monoids
We find on a monoid M the complex-valued solutions f, g : M → ℂ such that f is central and g is continuous of the functional equation f ( x σ ( y ) ) + f ( τ ( y ) x ) = 2 f ( x ) g ( y ) , x , y ∈ M , where σ : M → M is an involutive automorphism and τ : M → M is an involutive anti-automorphism. Th...
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| Veröffentlicht in: | Acta mathematica Sinica. English series 2022-08, Vol.38 (8), p.1303-1316 |
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| container_title | Acta mathematica Sinica. English series |
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| creator | Dimou, Hajira Elqorachi, Elhoucien Chahbi, Abdellatif |
| description | We find on a monoid
M
the complex-valued solutions
f, g : M
→ ℂ such that
f
is central and
g
is continuous of the functional equation
f
(
x
σ
(
y
)
)
+
f
(
τ
(
y
)
x
)
=
2
f
(
x
)
g
(
y
)
,
x
,
y
∈
M
,
where
σ
:
M
→
M
is an involutive automorphism and
τ
:
M
→
M
is an involutive anti-automorphism. The solutions are described in terms of multiplicative functions, additive functions and characters of 2-dimensional representations of
M
. |
| doi_str_mv | 10.1007/s10114-022-1233-0 |
| format | Article |
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M
the complex-valued solutions
f, g : M
→ ℂ such that
f
is central and
g
is continuous of the functional equation
f
(
x
σ
(
y
)
)
+
f
(
τ
(
y
)
x
)
=
2
f
(
x
)
g
(
y
)
,
x
,
y
∈
M
,
where
σ
:
M
→
M
is an involutive automorphism and
τ
:
M
→
M
is an involutive anti-automorphism. The solutions are described in terms of multiplicative functions, additive functions and characters of 2-dimensional representations of
M
.</description><identifier>ISSN: 1439-8516</identifier><identifier>EISSN: 1439-7617</identifier><identifier>DOI: 10.1007/s10114-022-1233-0</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Automorphisms ; Continuity (mathematics) ; Functional equations ; Mathematics ; Mathematics and Statistics ; Monoids</subject><ispartof>Acta mathematica Sinica. English series, 2022-08, Vol.38 (8), p.1303-1316</ispartof><rights>Springer-Verlag GmbH Germany & The Editorial Office of AMS 2022</rights><rights>Springer-Verlag GmbH Germany & The Editorial Office of AMS 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c198t-ad64d2143bb75c4589e1db7343b26e968fc095d6848e0716c4868882f53641513</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/s10114-022-1233-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10114-022-1233-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Dimou, Hajira</creatorcontrib><creatorcontrib>Elqorachi, Elhoucien</creatorcontrib><creatorcontrib>Chahbi, Abdellatif</creatorcontrib><title>A New Variant of Wilson’s Functional Equation on Monoids</title><title>Acta mathematica Sinica. English series</title><addtitle>Acta. Math. Sin.-English Ser</addtitle><description>We find on a monoid
M
the complex-valued solutions
f, g : M
→ ℂ such that
f
is central and
g
is continuous of the functional equation
f
(
x
σ
(
y
)
)
+
f
(
τ
(
y
)
x
)
=
2
f
(
x
)
g
(
y
)
,
x
,
y
∈
M
,
where
σ
:
M
→
M
is an involutive automorphism and
τ
:
M
→
M
is an involutive anti-automorphism. The solutions are described in terms of multiplicative functions, additive functions and characters of 2-dimensional representations of
M
.</description><subject>Automorphisms</subject><subject>Continuity (mathematics)</subject><subject>Functional equations</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Monoids</subject><issn>1439-8516</issn><issn>1439-7617</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp1kM9Kw0AQxhdRsFYfwFvA8-rM_o-3UloVql78c1zSZCMpNdvuJog3X8PX80nckoInYWCG4fu-GX6EnCNcIoC-igiIggJjFBnnFA7ICAXPqVaoD_ezkaiOyUmMKwApc1Ajcj3JHtxH9lKEpmi7zNfZa7OOvv35-o7ZvG_LrvFtsc5m277YjVmqe9_6poqn5Kgu1tGd7fuYPM9nT9Nbuni8uZtOFrTE3HS0qJSoWLq_XGpZCmlyh9VS87RgyuXK1CXkslJGGAcaVSmMMsawWnIlUCIfk4shdxP8tnexsyvfh_RUtEyDFgAcVFLhoCqDjzG42m5C816ET4tgd4jsgMgmRHaHyELysMETk7Z9c-Ev-X_TLw2bZuE</recordid><startdate>20220801</startdate><enddate>20220801</enddate><creator>Dimou, Hajira</creator><creator>Elqorachi, Elhoucien</creator><creator>Chahbi, Abdellatif</creator><general>Springer Berlin Heidelberg</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>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20220801</creationdate><title>A New Variant of Wilson’s Functional Equation on Monoids</title><author>Dimou, Hajira ; Elqorachi, Elhoucien ; Chahbi, Abdellatif</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c198t-ad64d2143bb75c4589e1db7343b26e968fc095d6848e0716c4868882f53641513</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Automorphisms</topic><topic>Continuity (mathematics)</topic><topic>Functional equations</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Monoids</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dimou, Hajira</creatorcontrib><creatorcontrib>Elqorachi, Elhoucien</creatorcontrib><creatorcontrib>Chahbi, Abdellatif</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>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>Acta mathematica Sinica. English series</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dimou, Hajira</au><au>Elqorachi, Elhoucien</au><au>Chahbi, Abdellatif</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A New Variant of Wilson’s Functional Equation on Monoids</atitle><jtitle>Acta mathematica Sinica. English series</jtitle><stitle>Acta. Math. Sin.-English Ser</stitle><date>2022-08-01</date><risdate>2022</risdate><volume>38</volume><issue>8</issue><spage>1303</spage><epage>1316</epage><pages>1303-1316</pages><issn>1439-8516</issn><eissn>1439-7617</eissn><abstract>We find on a monoid
M
the complex-valued solutions
f, g : M
→ ℂ such that
f
is central and
g
is continuous of the functional equation
f
(
x
σ
(
y
)
)
+
f
(
τ
(
y
)
x
)
=
2
f
(
x
)
g
(
y
)
,
x
,
y
∈
M
,
where
σ
:
M
→
M
is an involutive automorphism and
τ
:
M
→
M
is an involutive anti-automorphism. The solutions are described in terms of multiplicative functions, additive functions and characters of 2-dimensional representations of
M
.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s10114-022-1233-0</doi><tpages>14</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1439-8516 |
| ispartof | Acta mathematica Sinica. English series, 2022-08, Vol.38 (8), p.1303-1316 |
| issn | 1439-8516 1439-7617 |
| language | eng |
| recordid | cdi_proquest_journals_2707400306 |
| source | Springer Nature - Complete Springer Journals; Alma/SFX Local Collection |
| subjects | Automorphisms Continuity (mathematics) Functional equations Mathematics Mathematics and Statistics Monoids |
| title | A New Variant of Wilson’s Functional Equation on Monoids |
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