Best simultaneous monotone approximants in orlicz spaces

摘要

Let f = (f 1,., f m), where f j belongs to the Orlicz space [0, 1], and let w = (w 1,., w m) 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, 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.