
Let \(k\) be a positive constant and let \(X\) be a real normed space of dimension \(\geq 3\). Functions \(f:X\to X\) and \(g:X\times X\to R\) for which \(\| x-y\|=k\Rightarrow f(x)-f(y)=g(x,y)(x-y)\) are found.
conditional dilatation equation, Functional equations for functions with more general domains and/or ranges, conditional functional equation, normed space
conditional dilatation equation, Functional equations for functions with more general domains and/or ranges, conditional functional equation, normed space
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