Geodesic
Simultaneous Monotone Lp Approximation, p → ∞
Canadian mathematical bulletin, Tome 34 (1991) no. 3, pp. 343-350

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Suppose that f, g € L∞ [0,1 ] have discontinuities of the first kind only. Using the measure, max{ ∥f — h∥p, ∥g — h∥p}, of simultaneous Lp approximation, we show that the best simultaneous approximations f and g by nondecreasing functions converge uniformly as p → ∞. Part of the proof involves a discussion of discrete simultaneous approximation in a general context. Assuming only that f and g are approximately continuous, we show that their simultaneous best monotone Lp approximation is continuous.
DOI : 10.4153/CMB-1991-055-4
Mots-clés : 41A28, 40A05, 40A30, 41A30 
Huotari, Robert; Sahab, Salem. Simultaneous Monotone Lp Approximation, p → ∞. Canadian mathematical bulletin, Tome 34 (1991) no. 3, pp. 343-350. doi: 10.4153/CMB-1991-055-4
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     author = {Huotari, Robert and Sahab, Salem},
     title = {Simultaneous {Monotone} {Lp} {Approximation,} p {\textrightarrow} \ensuremath{\infty}},
     journal = {Canadian mathematical bulletin},
     pages = {343--350},
     year = {1991},
     volume = {34},
     number = {3},
     doi = {10.4153/CMB-1991-055-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-055-4/}
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