Set-valued orthogonal additivity
The author gives a form of solutions of the conditional Cauchy functional equation \[ F(x+y)=F(x)+F(y),\qquad x,y\in X,\; x\perp y, \] in the class of set-valued functions \(F:X\to cc(Y)\), where \((X, \perp )\) is an orthogonality space, \(Y\) is a Fréchet space and \(cc(Y)\) denotes the collection of all nonempty compact and convex subsets of \(Y\). Under some weaker assumptions on \(Y\) and the values of \(F\), she also studies the existence of appropriate selections of these solutions.
scientific article; zbMATH DE number 6477754
scientific article