Best Simultaneous Monotone Approximants in Orlicz Spaces

Abstract

Let f = (f1, , fm ), where fj belongs to the Orlicz space [0, 1], and let w = (w1, , wm ) be an m-tuple of m positive weights. If ⊂ [0, 1] is the class of nondecreasing functions, we denote by ,w(f, ) the set of best simultaneous monotone approximants to f, that is, all the elements g ∈ minimizing m j=1 1 0 (|fj − g |)wj, where is a convex function, (t) > 0 for t > 0, and (0) = 0. In this work, we show an explicit formula to calculate the maximum and minimum elements in ,w(f, ). In addition, we study the continuity of the best simultaneous monotone approximants.