New Pexiderizations of Drygas’ Functional Equation on Abelian Semigroups

Abstract Let ( S, +) be an abelian semigroup, let H, group which is uniquely 2-divisible, and ϕ endomorphism of S . We find the solutions f, h : → H each functional equations f ( x + y ) ϕ = h ∘ , ∈ S 2 \matrix{ {f\left( {x + y} \right) f\left( \varphi \left( y \right)} = h\left( x f \circ \right),\,x,y \in S,} \hfill \cr 2f\left( } in terms additive bi-additive maps. Moreover, as applications, we determine some related equations.