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Best Simultaneous Monotone Approximants in Orlicz Spaces

Author： Levis F. E.

Publisher： Taylor & Francis Ltd

ISSN： 0163-0563

Source： Numerical Functional Analysis and Optimization, Vol.34, Iss.1, 2013-01, pp. : 16-35

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

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Abstract

Let f = (f ₁,…, f _m), where f _j belongs to the Orlicz space L_φ[0, 1], and let w = (w ₁,…, w _m) be an m-tuple of m positive weights. If ⊂ L_φ[0, 1] is the class of nondecreasing functions, we denote by ℳ_{φ, w}(f, ) the set of best simultaneous monotone approximants to f, that is, all the elements g ∈ minimizing , where φ is a convex function, φ(t) > 0 for t > 0, and φ(0) = 0. In this work, we show an explicit formula to calculate the maximum and minimum elements in ℳ_{φ, w}(f, ). In addition, we study the continuity of the best simultaneous monotone approximants.

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