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On the cosine-sine functional equation on groups. (English) Zbl 1030.39026

The authors find the solutions \(f,g\in C(G)\) of each of the functional equations \[ \frac{f(x+y)\pm f(x+\sigma y)}{2}=f(x)g(y)+g(x)f(y)+h(x)h(y), \;\forall x,y\in G \] where \(G\) is a topological Abelian group, \(\sigma :G\longrightarrow G\) is a continuous involutive automorphism of \(G\), and where \(C(G)\) denotes the algebra of continuous, complex-valued functions on \(G\). These results generalize and extend the ones by J. K. Chung, Pl. Kannappan, and C. T. Ng [Linear Algebra Appl. 66, 259-277 (1985; Zbl 0564.39002)].

MSC:

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

Citations:

Zbl 0564.39002
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