Research Communication | Open Access
Volume 2021 | Communication ID 197
Volume 2021 | Communication ID 197
| The Drygas functional equation on abelian semigroups with endomorphisms |
Ahmed Akkaoui, Mohamed El Fatini, Brahim Fadli
Received |
Accepted |
Published |
January 31, 2021 |
February 15, 2021 |
March 15, 2021 |
Abstract: Let (S,+) be an abelian semigroup, let (H,+) be a uniquely 2- divisible, abelian group and let σ,τ be two endomorphisms of S. In this paper, we find the solutions f:S→H of the following Drygas type functional equation f(x+σ(y))+f(x+τ(y))=2f(x)+f(σ(y))+f(τ(y)), x,y∈S, in terms of additive and bi-additive maps. Further, we solve a partly Pexiderized version of the above equation and we use its solutions to determine the solutions of some related functional equations. In all results it is assumed that at least one of the endomorphisms σ and τ is surjective.