On an alternative functional equation related to the Cauchy equation
Copyright policy )On an alternative functional equation related to the Cauchy equation
We consider the following problem: Let (G, +) be an abelian group,B a complex Banach space,a, b∈B,b≠0,M a positive integer; find all functionsf:G →B such that for every (x, y) ∈G ×G the Cauchy differencef(x+y)−f(x)−f(y) belongs to the set {a, a+b, a+2b, ...,a+Mb}. We prove that all solutions of the above problem can be obtained by means of the injective homomorphisms fromG/H intoR/Z, whereH is a suitable proper subgroup ofG.
- DigiZeitschriften Germany
- University of Milan Italy
510.mathematics, complex Banach space, alternate equation, Abelian group, Cauchy equation, Cauchy difference, Functional equations for functions with more general domains and/or ranges, abelian group, Article, Functional equations and inequalities
510.mathematics, complex Banach space, alternate equation, Abelian group, Cauchy equation, Cauchy difference, Functional equations for functions with more general domains and/or ranges, abelian group, Article, Functional equations and inequalities
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