A generalization of the Cosine-Sine functional equation on a semigroup

2023/12/08 by Ajebbar, Omar, Elqorach, Elhoucien
#FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.2312.05285

Abstract

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

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