On maps characterized by action on equal products.

Abstract Let D be a division ring with characteristic different from 2. In this paper we will describe an additive map f satisfying the identity f (x) y + x f (y) = l for every x , y ∈ D such that x y = a , where l , a ∈ D and a is nonzero. Additionally, for nonzero m , k ∈ D , we will describe the additive bijection f satisfying the identity f (x) f (y) = m for every x , y ∈ D such that x y = k ; this description is the solution to a problem posed by Chebotar, Ke, Lee, and Shiao in 2005. [ABSTRACT FROM AUTHOR]