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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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+. |
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| ISSN: | 2314-8896 2314-8888 |