J Austral Math Soc Ser A 50 pp391--408, 1991.

Best Simultaneous Approximation of Quasi-Continuous Functions by Monotone Functions

Salem M. A. Sahab

Abstract

Let Q denote the Banach space (under the sup norm) of quasi-continuous functions on the unit interval [0, 1]. Let M denote the closed convex cone comprised of monotone nondecreasing functions on [0, 1]. For f and g in Q and 1 < p < ¥, let h_p denote the best L_p-simultaneous approximant of f and g by elements of M. It is shown that h_p converges uniformly as p ® ¥ to a best L_¥-simultaneous approximant of f and g by elements of M. However, this convergence is not true in general for any pair of bounded Lebesgue measurable functions. If f and g are continuous, then each h_p is continuous; so is lim_p®¥h_p = h_¥.

1980 AMS Subject Classification (1985 Revision): primary 41A28; secondary 41A30, 41A65

Browse the article

Authors

Salem M. A. Sahab

King Abdulaziz University, P.O. Box 9028, Jeddah 21413, Saudi Arabia.