Jensen’s and the quadratic functional equations with an endomorphism
Copyright policy )Jensen’s and the quadratic functional equations with an endomorphism
We determine the solutions f : S → H of the generalized Jensen’s functional equation f (x + y) + f (x + φ(y)) = 2f (x), x,y ∈ S,and the solutions f : S → H of the generalized quadratic functional equation f (x + y) + f (x + φ(y)) = 2f (x) + 2f (y), x,y ∈ S,where S is a commutative semigroup, H is an abelian group (2-torsion free in the first equation and uniquely 2-divisible in the second) and φ is an endomorphism of S.
Jensen, additive function, semigroup, Functional equations for functions with more general domains and/or ranges, quadratic, additive func-tion, functional equation, Functional equation
Jensen, additive function, semigroup, Functional equations for functions with more general domains and/or ranges, quadratic, additive func-tion, functional equation, Functional equation
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