Best Simultaneous Monotone Approximants in Orlicz Spaces

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