On a generalization of the Cauchy functional equation
Copyright policy )On a generalization of the Cauchy functional equation
The paper deals with the functional equation \(g(ax+by) =Ag(x)+Bg(y) +L(x,y)\) where \(g\) maps a nonempty subset \(P\) of a vector space \(X\), satisfying the condition \(aP+bP \subset P\), into a vector space \(Y\), and \(L:X \times X \to Y\) is a given biadditive mapping. The main result yields a necessary and sufficient condition (relating \(a,b,A,B\) and \(L\) and concerning algebraic properties of \(P)\) in order to assure that the equation above has a solution. Moreover, the general form of the solutions is given.
- DigiZeitschriften Germany
- Pedagogical University of Kraków Poland
- Pedagogical University Mozambique
510.mathematics, Functional equations for real functions, Cauchy functional equation, general form of the solutions, vector space, Functional equations for functions with more general domains and/or ranges, biadditive mapping, Functional equations for complex functions, Article, generalization
510.mathematics, Functional equations for real functions, Cauchy functional equation, general form of the solutions, vector space, Functional equations for functions with more general domains and/or ranges, biadditive mapping, Functional equations for complex functions, Article, generalization
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