Applications of Orlicz-Lorentz Spaces in Gateaux Differentiability

Abstract

This study aimed to study Gateaux differentiability of the functional   and of the Luxemburg norm, it followed the descriptive method and the study found that we can obtain the one-sided Gateaux derivatives in both cases by characterizing those points where the Gateaux derivative of the norm exists, we obtain a characterization of best -approximants  from convex closed subsets, there a relation between best -approximants and best approximants from a convex set.