In [7] D. G. Moursund examined the problem of approximating xliz over an interval [a, b] (a > 0) by applying the Newton-Raphson iteration scheme to classes of polynomial and rational approximants. G. Meinardus and G. D. Taylor [6] have observed that the above problem may be posed in a more general setting and the results obtained by Moursund extended to the approximation of additional functions. Specifically, given a compact subset X of [a, b], let C(X) denote the space of all continuous real-valued functions defined on X normed by llfll = max(I w(x)f(x)i: x E X}, where w E C(X) and w > 0 on X. Let K be a convex subset of C(X) and @ a continuous mapping of K into C(X). The problem of interest was then to approximate g E @b(K) by elements of Q(M) where M is a subset of K consisting of members of a Haar subspace of C[a, b]. By imposing certain restrictions on CD, K and Al, Meinardus and Taylor were able to develop a theory for the above nonlinear approximation problem which is analogous to the classical Chebyshev theory. Moreover they were able to obtain results similar to those of P. H. Sterbenz and C. T. Fike [13] and R. F. King and D. L. Phillips [2] in the more general setting. Since the theory obtained has application to many iterative processes that can be used to approximate functions such as eX, In x and xlkil, IZ = 2, 3 ,... the following definition is made: