Best monotone approximation in 𝐿₁[0,1]

Huotari, Robert; Legg, David A.

doi:10.1090/s0002-9939-1985-0784179-x

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Simultaneous Monotone Zi-approximation1

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1987

1993

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Cited by 8 publications

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“…In [5], it was shown that the set of best ii-approximations to a bounded measurable function / by nondecreasing functions includes its supremum and infimum. However, this is not the case with f*i(f,g;M).…”

Section: Simultaneous Monotone Zi-approximationmentioning

confidence: 99%

Simultaneous monotone approximation in low-order mean

Huotari

Sahab

1992

Bull. Austral. Math. Soc.

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Suppose that /, g £ Loo [0,1] have discontinuities of the first kind only. Using the measure, max{||/ -h\\ , \\g -h\\ p }, of simultaneous L p approximation, we show that the best simultaneous approximations, h p , to / and g by nondecreasing functions converge uniformly as p -» 1. Part of the proof involves a discussion of discrete simultaneous approximation in a general context. We discuss the inheritance of properties of / and g by h p , and of h p by hi.

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Section: Simultaneous Monotone Zi-approximationmentioning

confidence: 99%