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,...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 norm展开更多
文摘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 norm
