SemOpenAlex |

SemOpenAlex

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1884562202> ?p ?o ?g. }

Showing items 1 to 60 of 60 with 100 items per page.

W1884562202 endingPage "7" @default.
W1884562202 startingPage "1" @default.
W1884562202 abstract "Let<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:math>and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>be a commutative semigroup and a commutative group, respectively,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mrow><mml:mi mathvariant=double-struck>C</mml:mi></mml:mrow></mml:math>and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant=double-struck>R</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>the sets of complex numbers and nonnegative real numbers, respectively, and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mi>σ</mml:mi><mml:mo>:</mml:mo><mml:mi>S</mml:mi><mml:mo>→</mml:mo><mml:mi>S</mml:mi></mml:math>or<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mi>σ</mml:mi><mml:mo>:</mml:mo><mml:mi>G</mml:mi><mml:mo>→</mml:mo><mml:mi>G</mml:mi></mml:math>an involution. In this paper, we first investigate general solutions of the functional equation<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mi>f</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>x</mml:mi><mml:mo>+</mml:mo><mml:mi>σ</mml:mi><mml:mi>y</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mi>g</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>y</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>-</mml:mo><mml:mi>g</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>y</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>for all<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>∈</mml:mo><mml:mi>S</mml:mi></mml:math>, where<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M9><mml:mi>f</mml:mi><mml:mo>,</mml:mo><mml:mi>g</mml:mi><mml:mo>:</mml:mo><mml:mi>S</mml:mi><mml:mo>→</mml:mo><mml:mi mathvariant=double-struck>C</mml:mi></mml:math>. We then prove the Hyers-Ulam stability of the functional equation; that is, we study the functional inequality<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M10><mml:mo stretchy=false>|</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>x</mml:mi><mml:mo>+</mml:mo><mml:mi>σ</mml:mi><mml:mi>y</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>-</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mi>g</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>y</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>+</mml:mo><mml:mi>g</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>y</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo stretchy=false>|</mml:mo><mml:mo>≤</mml:mo><mml:mi>ψ</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>y</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>for all<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M11><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>∈</mml:mo><mml:mi>G</mml:mi></mml:math>, where<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M12><mml:mi>f</mml:mi><mml:mo>,</mml:mo><mml:mi>g</mml:mi><mml:mo>:</mml:mo><mml:mi>G</mml:mi><mml:mo>→</mml:mo><mml:mi mathvariant=double-struck>C</mml:mi></mml:math>and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M13><mml:mi>ψ</mml:mi><mml:mo>:</mml:mo><mml:mi>G</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=double-struck>R</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math>." @default.
W1884562202 created "2016-06-24" @default.
W1884562202 creator A5018578747 @default.
W1884562202 creator A5067284133 @default.
W1884562202 creator A5076360253 @default.
W1884562202 date "2015-01-01" @default.
W1884562202 modified "2023-09-26" @default.
W1884562202 title "Ulam-Hyers Stability of Trigonometric Functional Equation with Involution" @default.
W1884562202 cites W1539244578 @default.
W1884562202 cites W2003874621 @default.
W1884562202 cites W2009266073 @default.
W1884562202 cites W2012981171 @default.
W1884562202 cites W2014796937 @default.
W1884562202 cites W2052339276 @default.
W1884562202 cites W2054790994 @default.
W1884562202 cites W2118569170 @default.
W1884562202 cites W2123304375 @default.
W1884562202 cites W2128668476 @default.
W1884562202 cites W2148074288 @default.
W1884562202 cites W4210945509 @default.
W1884562202 cites W4255740457 @default.
W1884562202 doi "https://doi.org/10.1155/2015/742648" @default.
W1884562202 hasPublicationYear "2015" @default.
W1884562202 type Work @default.
W1884562202 sameAs 1884562202 @default.
W1884562202 citedByCount "1" @default.
W1884562202 countsByYear W18845622022017 @default.
W1884562202 crossrefType "journal-article" @default.
W1884562202 hasAuthorship W1884562202A5018578747 @default.
W1884562202 hasAuthorship W1884562202A5067284133 @default.
W1884562202 hasAuthorship W1884562202A5076360253 @default.
W1884562202 hasBestOaLocation W18845622021 @default.
W1884562202 hasConcept C11413529 @default.
W1884562202 hasConcept C154945302 @default.
W1884562202 hasConcept C41008148 @default.
W1884562202 hasConceptScore W1884562202C11413529 @default.
W1884562202 hasConceptScore W1884562202C154945302 @default.
W1884562202 hasConceptScore W1884562202C41008148 @default.
W1884562202 hasFunder F4320322120 @default.
W1884562202 hasLocation W18845622021 @default.
W1884562202 hasLocation W18845622022 @default.
W1884562202 hasOpenAccess W1884562202 @default.
W1884562202 hasPrimaryLocation W18845622021 @default.
W1884562202 hasRelatedWork W2051487156 @default.
W1884562202 hasRelatedWork W2052122378 @default.
W1884562202 hasRelatedWork W2053286651 @default.
W1884562202 hasRelatedWork W2073681303 @default.
W1884562202 hasRelatedWork W2317200988 @default.
W1884562202 hasRelatedWork W2544423928 @default.
W1884562202 hasRelatedWork W2947381795 @default.
W1884562202 hasRelatedWork W2181413294 @default.
W1884562202 hasRelatedWork W2181743346 @default.
W1884562202 hasRelatedWork W2187401768 @default.
W1884562202 hasVolume "2015" @default.
W1884562202 isParatext "false" @default.
W1884562202 isRetracted "false" @default.
W1884562202 magId "1884562202" @default.
W1884562202 workType "article" @default.