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Simultaneous Monotone Lp Approximation, p → ∞

Published online by Cambridge University Press:  20 November 2018

Robert Huotari  and
Salem Sahab
Robert Huotari
Affiliation:
Department of Mathematics, Idaho State University, Pocatello, Idaho, USA 83209 Internet: [email protected]
Salem Sahab
Affiliation:
Mathematics Department, King Abdulaziz University, Jeddah 214I3, Saudi Arabia
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Abstract

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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.

Keywords

41A2840A0540A3041A30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 3 , 01 September 1991 , pp. 343 - 350
Copyright
Copyright © Canadian Mathematical Society 1991

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