A note on the approximation of linear and affine functions: The case of bounded slope
One considers a set S of pairs (x,C), with x a point in n-dimensional space and C a convex subset of k-dimensional space. Criteria are given for the existence of a linear or affine function f such that for each (x,C) in S, f(x) is in C, with the further constraint that f must belong to a given convex set K of functions (for example, those having their slope within certain bounds). This generalizes the author's paper in Archiv Math. 46, 371-384 (1986; Zbl 0566.52003), where no such constraint was imposed on f. The main results are applied to the problem of digitizing hyperplanes.
scientific article; zbMATH DE number 4098182