On the Uniqueness of Best Non-decreasing Approximation in Orlicz Spaces

Abstract

Given an approximately continuous function $f$ in an Orlicz space $L^{\Phi }([a,b]),$ for a suitable class of convex functions $\Phi ,$ we employ a characterization of the best monotone approximation set to establish its continuity, which in turn yields the uniqueness property for the best monotone approximation in $L^{\Phi }([a,b]).$