On the monotone simultaneous approximation on [0, 1]
1988 ◽
Vol 38
(3)
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pp. 401-411
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Keyword(s):
Let Ω denote the closed interval [0, 1] and let bA denote the set of all bounded, approximately continuous functions on Ω. Let Q denote the Banach space (sup norm) of quasi-continuous functions on Ω. Let M denote the closed convex cone in Q comprised of non-decreasing functions. Let hp, 1 < p < ∞, denote the best Lp-simultaneaous approximation to the bounded measurable functions f and g by elements of M. It is shown that if f and g are elements of Q, then hp converges unifornily to a best L1-simultaneous approximation of f and g. We also show that if f and g are in bA, then hp is continuous.
1991 ◽
Vol 50
(3)
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pp. 391-408
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1997 ◽
Vol 55
(1)
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pp. 147-160
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Keyword(s):
2003 ◽
Vol 13
(07)
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pp. 1877-1882
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Keyword(s):
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1989 ◽
Vol 40
(1)
◽
pp. 37-48
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2005 ◽
Vol 2005
(17)
◽
pp. 2749-2756
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Keyword(s):