CONSTRAINED L(P)-APPROXIMATION BY GENERALIZED N-CONVEX FUNCTIONS INDUCED BY ECT-SYSTEMS

The problem of finding a best L(p),-approximation (1 less than or equa l to p < infinity) to a function in L(p) from a special subcone of gen eralized it-convex functions induced by an ECT-system is considered. T chebycheff splines with a countably infinite number of knots are intro duced and best approximations are characterized in terms of local best approximations by these splines. Various properties of best approxima tions and their uniqueness in L(1) are investigated. Some special resu lts for generalized monotone and convex cases are obtained. (C) 1995 A cademic Press, Inc.