Stability of a Bi-Additive Functional Equation in Banach Modules Over a C⋆-Algebra
We solve the bi-additive functional equation f(x+y,z−w)+f(x−y,z+w)=2f(x,z)−2f(y,w) and prove that every bi-additive Borel function is bilinear. And we investigate the stability of a bi-additive functional equation in Banach modules over a unital C⋆-algebra.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/835893 |
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| author | Won-Gil Park Jae-Hyeong Bae |
| author_facet | Won-Gil Park Jae-Hyeong Bae |
| author_sort | Won-Gil Park |
| collection | DOAJ |
| description | We solve the bi-additive functional equation f(x+y,z−w)+f(x−y,z+w)=2f(x,z)−2f(y,w) and prove that every bi-additive Borel function is bilinear. And we investigate the stability of a bi-additive functional equation in Banach modules over a unital C⋆-algebra. |
| format | Article |
| id | doaj-art-25c3952e54974cf393f0cfccc5048589 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-25c3952e54974cf393f0cfccc50485892025-02-03T05:45:42ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/835893835893Stability of a Bi-Additive Functional Equation in Banach Modules Over a C⋆-AlgebraWon-Gil Park0Jae-Hyeong Bae1Department of Mathematics Education, College of Education, Mokwon University, Daejeon 302-729, Republic of KoreaGraduate School of Education, Kyung Hee University, Yongin 446-701, Republic of KoreaWe solve the bi-additive functional equation f(x+y,z−w)+f(x−y,z+w)=2f(x,z)−2f(y,w) and prove that every bi-additive Borel function is bilinear. And we investigate the stability of a bi-additive functional equation in Banach modules over a unital C⋆-algebra.http://dx.doi.org/10.1155/2012/835893 |
| spellingShingle | Won-Gil Park Jae-Hyeong Bae Stability of a Bi-Additive Functional Equation in Banach Modules Over a C⋆-Algebra Discrete Dynamics in Nature and Society |
| title | Stability of a Bi-Additive Functional Equation in Banach Modules Over a C⋆-Algebra |
| title_full | Stability of a Bi-Additive Functional Equation in Banach Modules Over a C⋆-Algebra |
| title_fullStr | Stability of a Bi-Additive Functional Equation in Banach Modules Over a C⋆-Algebra |
| title_full_unstemmed | Stability of a Bi-Additive Functional Equation in Banach Modules Over a C⋆-Algebra |
| title_short | Stability of a Bi-Additive Functional Equation in Banach Modules Over a C⋆-Algebra |
| title_sort | stability of a bi additive functional equation in banach modules over a c⋆ algebra |
| url | http://dx.doi.org/10.1155/2012/835893 |
| work_keys_str_mv | AT wongilpark stabilityofabiadditivefunctionalequationinbanachmodulesoveracalgebra AT jaehyeongbae stabilityofabiadditivefunctionalequationinbanachmodulesoveracalgebra |