BEST MONOTONE L_■-APPROXIMATIONS IN SEVERAL VARIABLES  

作　　者：Miguel Iturrieta Felipe Zó 

机构地区：[1]Universidad Nac.del Comahue,Argentina [2]Conicet and Univ.Nac.de San Luis,Argentina

出　　处：《Analysis in Theory and Applications》1998年第3期1-10,共10页分析理论与应用（英文刊）

摘　　要：Given a continuous function f defined on the unit cube of R^n and a convex function _t,_t(0)-0,_t(x)>0,for x>0,we prove that the set of best L^(t)-approximations by monotone functions has exactly one element ft,which is also a continuous function.Moreover if the family of convex functions {_t}t>0 converges uniformly on compact sets to a function _0, then the best approximation f_t→f_0 uniformly,as t→0,where fo is the best approximation of f within the Orlicz space L^(0) The best approxima- tions{f_t}are obtained as well as minimizing integrals or the Luxemburg normGiven a continuous function f defined on the unit cube of R^n and a convex function _t,_t(0)-0,_t(x)>0,for x>0,we prove that the set of best L^(t)-approximations by monotone functions has exactly one element ft,which is also a continuous function.Moreover if the family of convex functions {_t}t>0 converges uniformly on compact sets to a function _0, then the best approximation f_t→f_0 uniformly,as t→0,where fo is the best approximation of f within the Orlicz space L^(0) The best approxima- tions{f_t}are obtained as well as minimizing integrals or the Luxemburg norm

关 键 词：APPROXIMATIONS IN SEVERAL VARIABLES BEST MONOTONE L 

分 类 号：O241[理学—计算数学]