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Simultaneous monotone approximation in low-order mean

Published online by Cambridge University Press:  17 April 2009

Robert Huotari  and
Salem Sahab
Robert Huotari
Affiliation:
Department of MathematicsIdaho State University Pocatello, ID 83209United States of America
Salem Sahab
Affiliation:
Mathematics DepartmentKing Abdulaziz UniversityJeddah 21413Saudi 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, hp, to f 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 f and g by hp, and of hp by h1.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 3 , June 1992 , pp. 423 - 437
Copyright
Copyright © Australian Mathematical Society 1992

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