Ulam-Hyers Stability of Trigonometric Functional Equation with Involution
Let S and G be a commutative semigroup and a commutative group, respectively, C and R+ the sets of complex numbers and nonnegative real numbers, respectively, and σ:S→S or σ:G→G an involution. In this paper, we first investigate general solutions of the functional equation f(x+σy)=f(x)g(y)-g(x)f(y)...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/742648 |
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| author | Jaeyoung Chung Chang-Kwon Choi Jongjin Kim |
| author_facet | Jaeyoung Chung Chang-Kwon Choi Jongjin Kim |
| author_sort | Jaeyoung Chung |
| collection | DOAJ |
| description | Let S and G be a commutative semigroup and a commutative group, respectively, C and R+ the sets of complex numbers and nonnegative real numbers, respectively, and σ:S→S or σ:G→G an involution. In this paper, we first investigate general solutions of the functional equation f(x+σy)=f(x)g(y)-g(x)f(y) for all x,y∈S, where f,g:S→C. We then prove the Hyers-Ulam stability of the functional equation; that is, we study the functional inequality |f(x+σy)-f(x)g(y)+g(x)f(y)|≤ψ(y) for all x,y∈G, where f,g:G→C and ψ:G→R+. |
| format | Article |
| id | doaj-art-11c8c1b101cb43ad9fcbd512573951ba |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-11c8c1b101cb43ad9fcbd512573951ba2025-02-03T06:13:39ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/742648742648Ulam-Hyers Stability of Trigonometric Functional Equation with InvolutionJaeyoung Chung0Chang-Kwon Choi1Jongjin Kim2Department of Mathematics, Kunsan National University, Kunsan 573-701, Republic of KoreaDepartment of Mathematics, Chonbuk National University, Jeonju 561-756, Republic of KoreaDepartment of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju 561-756, Republic of KoreaLet S and G be a commutative semigroup and a commutative group, respectively, C and R+ the sets of complex numbers and nonnegative real numbers, respectively, and σ:S→S or σ:G→G an involution. In this paper, we first investigate general solutions of the functional equation f(x+σy)=f(x)g(y)-g(x)f(y) for all x,y∈S, where f,g:S→C. We then prove the Hyers-Ulam stability of the functional equation; that is, we study the functional inequality |f(x+σy)-f(x)g(y)+g(x)f(y)|≤ψ(y) for all x,y∈G, where f,g:G→C and ψ:G→R+.http://dx.doi.org/10.1155/2015/742648 |
| spellingShingle | Jaeyoung Chung Chang-Kwon Choi Jongjin Kim Ulam-Hyers Stability of Trigonometric Functional Equation with Involution Journal of Function Spaces |
| title | Ulam-Hyers Stability of Trigonometric Functional Equation with Involution |
| title_full | Ulam-Hyers Stability of Trigonometric Functional Equation with Involution |
| title_fullStr | Ulam-Hyers Stability of Trigonometric Functional Equation with Involution |
| title_full_unstemmed | Ulam-Hyers Stability of Trigonometric Functional Equation with Involution |
| title_short | Ulam-Hyers Stability of Trigonometric Functional Equation with Involution |
| title_sort | ulam hyers stability of trigonometric functional equation with involution |
| url | http://dx.doi.org/10.1155/2015/742648 |
| work_keys_str_mv | AT jaeyoungchung ulamhyersstabilityoftrigonometricfunctionalequationwithinvolution AT changkwonchoi ulamhyersstabilityoftrigonometricfunctionalequationwithinvolution AT jongjinkim ulamhyersstabilityoftrigonometricfunctionalequationwithinvolution |