2022/10/12 by Aserrar, Youssef, Elqorachi, Elhoucien
#39B32 #39B52 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2210.06181
In this paper, we determine the complex-valued solutions of the following functional equations g(xσ(y)) = g(x)g(y)+f(x)f(y), x,y∈ S,f(xσ(y)) = f(x)g(y)+f(y)g(x), x,y∈ S,f(xσ(y)) = f(x)g(y)+f(y)g(x)-g(x)g(y), x,y∈ S,f(xσ(y))=f(x)g(y)+f(y)g(x)+αg(xσ(y)), x,y∈ S,f(xσ(y))=f(x)g(y)-f(y)g(x)+αg(xσ(y)), x,y∈ S, where S is a semigroup, α∈ ℂ\backslash \lbrace 0\rbrace is a fixed constant and σ:S→ S an involutive automorphism.