2023/12/08 by Jafar, Ahmed, Ajebbar, Omar, Elqorachi, Elhoucien
#FOS: Mathematics #General Mathematics (math.GM)
paper · doi:10.48550/arxiv.2401.06147
Let S be a semigroup, z0 a fixed element in S and σ:S \longrightarrow S an involutive automorphism. We determine the complex-valued solutions of Kannappan-sine subtraction law f(xσ(y)z0)=f(x)g(y)-f(y)g(x), x,y ∈ S. As an application we solve the following variant of Kannappan-sine subtraction law viz. f(xσ(y)z0)=f(x)g(y)-f(y)g(x)+λg(xσ(y)z0) , x,y ∈ S, where λ∈ ℂ*. The continuous solutions on topological semigroups are given and an example to illustrate the main results is also given.