A uniqueness theorem of a system of nonlinear equations and its applications (Q2343570)

In this paper, a fairly simple theorem for finding a unique solution to a system of non-linear equations is proven. Using this theorem, the author provides simple proofs for theorems on the uniqueness of a power orthogonal polynomial, and the existence and uniqueness of a Gaussian quadrature formula for an extended Chebyshev system. While both of these results were previously known, a proof is given on the existence of a Gaussian-Birkhoff quadrature formula which improves a known result by relaxing some of the conditions for the existence.