New Pexiderizations of Drygas’ functional equation on abelian semigroups
Abstract
Let (S,+) be an abelian semigroup, let (H,+) be an abelian group which is uniquely 2-divisible, and let ϕ be an endomorphism of S. We find the solutions f,h: S→H of each of the functional equations
f(x+y) + f(x+ϕ(y)) = h(x) + f(y) + f◦ϕ(y), x,y∈S,
f(x+y) + f(x+ϕ(y)) = h(x) + 2f(y), x,y∈S,
in terms of additive and bi-additive maps. Moreover, as applications, we determine the solutions of some related functional equations.
Keywords
Pexider; Drygas functional equation; quadratic; symmetric bi-additive function; additive function; semigroup; endomorphism
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Department of Mathematics E.N.S.A.M, Moulay ISMAIL University, Meknes Morocco
https://orcid.org/0000-0003-3708-3164
Department of Mathematics E.N.S.A.M, Moulay ISMAIL University, Meknes Morocco
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