Best Simultaneous approximation of quasi-continuous functions by monotone functions

Journal of the Australian Mathematical Society

Salem M. A. Sahab¹ 

关键词: primary 41 A 28;    secondary 41 A 30;    41 A 65;   

DOI  :  10.1017/S1446788700032997

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

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 hp denote the best Lp-simultaneous approximant of f and g by elements of ℳ. It is shown that hp 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 hp is continuous; so is limp→∞ hp = h∞.

【 授权许可】

Unknown