A generalization of the Cosine-Sine functional equation on a semigroup
Abstract
Given a semigroup S equipped with an involutive automorphism σ, we determine the complex-valued solutions f,g,h of the functional equation equation*f(xσ(y))=f(x)g(y)+g(x)f(y)+h(x)h(y),\,\,x,y∈ S,equation* in terms of multiplicative functions and solutions of the special cases of sine and cosine-sine functional equations.
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