Myron S Henry

Lipschitz and strong unicity constants for changing dimension

;I Tf,}& with lim,,m /! f -h 11 = 0 that lim,+, A(h) = h(f). For fixed f and n, Henry and Roulier [5] investigate the behavior of X(f) for changing intervals.

Applications of approximation theory to the initial value problem

In recent years, several papers have been devoted to best approximating in some sense the solutions to various types of nonlinear differential and integro-differential equations (see, for example, [I, 4, 7-91). These papers are generally concerned with proving that a best approximation exists and with showing that an appropriate sequence of best approximations converges to a solution of the differential or integro-differential equation. In the previously mentioned references, the best approximation problem is ordinarily nonlinear and consequently computational techniques are not readily available. In this paper we propose to reexamine the best approximation problem as posed in [I, 4, 7-91 and discuss alternatives that may result in computationally obtainable best approximations. Although our discussion is limited to the initial value problem IVP

Continuity theorems for the rational product approximation operator

Abstract This paper establishes that the rational product approximation operator is continuous. Under an additional restriction, this operator satisfies a local Lipschitz condition.