2020/10/07 by Abdellatif Chahbi, Abdellatif, Chahbi, Elhoucien Elqorachi +1
Mathematics · #Functional Equations Stability Results #Advanced Topics in Algebra #Advanced Topology and Set Theory
paper · pdf · doi:10.48550/arxiv.2010.03974
In this paper, we determine the complex-valued solutions of the functional equation f(xσ(y))+f(τ(y)x)=2f(x)f(y) for all x,y ∈ M, where M is a monoid, σ: M\longrightarrow M is an involutive automorphism and τ: M\longrightarrow M is an involutive anti-automorphism. The solutions are expressed in terms of multiplicative functions, and characters of 2-dimensional irreducible representations of M.