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On the monotone simultaneous approximation on [0, 1]

Published online by Cambridge University Press:  17 April 2009

Salem M.A. Sahab
Salem M.A. Sahab
Affiliation:
Mathematics Department, King Abdulaziz University, P.O. Box 9028, Jeddah 21413, Saudi Arabia
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 38 , Issue 3 , December 1988 , pp. 401 - 411
Copyright
Copyright © Australian Mathematical Society 1988

References

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