Abstract
AbstractLet Λw,ϕ be the Orlicz–Lorentz space. We study Gateaux differentiability of the functional ψw,ϕ (f) = $ \int _{0} ^{\infty} $ ϕ (f *)w and of the Luxemburg norm. More precisely, we obtain the one‐sided Gateaux derivatives in both cases and we characterize those points where the Gateaux derivative of the norm exists. We give a characterization of best ψw,ϕ ‐approximants from convex closed subsets and we establish a relation between best ψw,ϕ ‐approximants and best approximants from a convex set. A characterization of best constant ψw,ϕ ‐approximants and the algorithm to construct the best constant for maximum and minimum ψw,ϕ ‐pproximants are given. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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