Best simultaneous monotone approximation in Orlicz spaces

F.E. LEVIS; M. MARANO

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION

TAYLOR & FRANCIS INC

Lugar: Philadelphia; Año: 2013 vol. 34 p. 16 - 35

0163-0563

Let f=(f_1,...,f_m), where f_j belongs to the Orlicz space L_phi[0,1], and let w=(w_1,...,w_m) be an m-tuple of m positive weights. If D c L_phi[0,1] is the class of nondecreasing functions, we denote by M_{phi,w}(f,D) the set of best simultaneous monotone approximants to f, i.e., all the elements g in D minimizing sum_{j=1}^m int_0^1 phi(|f_j-g|)w_j, where phi is a convex function. In this work we show an explicit formula to calculate the maximum and minimum elements in M_ {phi,w}(f,D). In addition, we study the continuity of the best simultaneous monotone approximants.