## On a quadratic-trigonometric functional equation and some applications.(English)Zbl 0830.39014

Trans. Am. Math. Soc. 347, No. 4, 1131-1161 (1995); erratum ibid. 349, No. 11, 4691 (1997).
In the process of obtaining the general solutions (which are five in number) of (FE) $$f_1(xy) + f_2(xy^{-1}) = f_3(x) + f_4(y) + f_5(x) f_6(y)$$ under the condition $$(*)$$ $$f_i(xyz)= f_i (xzy)$$ $$(i = 1,2)$$ where $$f_i$$’s are complex valued functions on a group, the authors obtain the general solutions of many functional equations including $$f(xy) + f(xy^{-1}) = p(x) + p(y) + q(x) h(y)$$ and $$f(xy) - f(xy^{-1}) = k(x) + h(x)g(y)$$ where $$f$$ satisfies $$(*)$$. Special cases of (FE) include the Pexider, quadratic, d’Alembert and Wilson equations.

### MSC:

 39B52 Functional equations for functions with more general domains and/or ranges 39B32 Functional equations for complex functions
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### References:

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