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Quadratic Differences that Depend on the Product of Arguments |
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| Authors: | J K Chung B R Ebanks C T Ng P K Sahoo W B Zeng |
| Institution: | 1. Department of Applied Mathematics, South China University of Technology, Guangzhou, People’s Republic of China 2. Department of Mathematics Marshall University, Huntington, West Virginia, 25755-2560, USA 3. Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada 4. Department of Mathematics, University of Louisville, Louisville, Kentucky, 40292-0001, USA |
| Abstract: | In this paper, we determine all functions ?, defined on a field K (belonging to a certain class) and taking values in an abelian group, such that the quadratic difference ?(x + y) + ?(x ? y) ? 2?(x) ? 2?(y) depends only on the product xy for all x, y ∈ K. Using this result, we find the general solution of the functional equation ?1(x + y) + ?2(x ? y) = ?3(x) + ?4(y) + g(xy). |
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