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Simultaneous monotone approximation in low-order mean

Published online by Cambridge University Press:  17 April 2009

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, gL[0,1] have discontinuities of the first kind only. Using the measure, max{‖fhp, ‖ghp}, 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
Copyright
Copyright © Australian Mathematical Society 1992

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