The error in discrete Φ-approximation

✍ Scribed by F.E. Levis

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 533 KB
• Volume: 34
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/s0895-7177(01)00076-0

✦ Synopsis

Let q3 : [0, 00) + [O,oo) be a convex function 4(z) > 0, if I > 0, 4(O) = 0 and let (n,A, p) be a measure space, where fl = N or a finite subset of N, A = 2", and ~1 is any finite measure. We consider the set k&w(f) of best monotone &approximates of the function f in the Orlicz space L+ = Ld(R, A,p). We obtain a best +-approximant as limit of one sequence of best approximates in finite dimension. Also, we give a computational algorithm to estimate the error in +-approximation of functions in the subspace LT, by nondecreasing functions.