On nonuniqueness in rational Lp-approximation

AbstractThe method described by I. Diener [3] is applied to rational functions rather than to families with one nonlinear parameter. Given an (m + 2)-dimensional subspace of Lp, a function with two or more nearest points in Rnm is obtained by the Borsuk antipodality theorem, if n > 0 and some exceptional cases arc excluded. Moreover, a symmetry argument leads to functions with at least four global solutions