Uniqueness for monotone reciprocals
Let X be a closed subset of an interval and let P be a linear subspace of C(X). Let \(R=\{1/p:\) 1/p is monotone increasing on X, \(p>0\) and X,p\(\in P\}\). The author shows that if best approximation by monotone decreasing elements of P is unique, then best approximation by elements of R is also unique. The proof uses techniques developed by the author in Trans. Am. Math. Soc. 136, 151-157 (1969; Zbl 0172.343) and Approximation theory IV, Proc. int. Conf., Tex. A \& M Univ. 1983, 441-444 (1983; Zbl 0541.41027).
scientific article; zbMATH DE number 4190365