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

Chung, J. K.; Ebanks, B. R.; Ng, C. T.; Sahoo, P. K.

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.

Reviewer: Pl.Kannappan (Waterloo/Ontario)

MSC:

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

Keywords:

quadratic-trigonometric functional equation; Pexider equation; d’Alembert equation; complex valued functions on a group; general solutions; Wilson equations

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