Constrained Lp-Approximation by Generalized n-Convex Functions Induced by ECT-Systems Original Research Article

The problem of finding a best Lp-approximation (1 ≤ p < ∞) to a function in Lp from a special subcone of generalized n-convex functions induced by an ECT-system is considered. Tchebycheff splines with a countably infinite number of knots are introduced and best approximations are characterized in terms of local best approximations by these splines. Various properties of best approximations and their uniqueness in L1 are investigated. Some special results for generalized monotone and convex cases are obtained.