Construction of the Best Monotone Approximation on Lp [0, 1]

Authors

J. J. Swetits, Old Dominion University
S. E. Weinstein, Old Dominion University

Document Type

Article

Publication Date

1990

DOI

10.1016/0021-9045(90)90028-o

Publication Title

Journal of Approximation Theory

Volume

61

Issue

1

Pages

118-130

Abstract

(First paragraph) For 1 ≤ p < ∞, let L_p, denote the Banach space of pth power Lebesgue integrable functions on [0, l] ∥ƒ∥_p = (∫¹₀∣ƒ∣ ^p)^1/p Let M_p denote the set of nondecreasing functions in L_p. For l < p < ∞ , each ƒ∊L_p has a unique best approximation from M_p, while, for p = 1, existence of a best approximation from M₁ follows from Proposition 4 of [6].

Comments

Web of Science: "Free full-text from publisher -- Elsevier open archive."

Copyright © 1990 Published by Elsevier Inc.

Original Publication Citation

Swetits, J. J., & Weinstein, S. E. (1990). Construction of the best monotone-approximation on Lp [0,1]. Journal of Approximation Theory, 61(1), 118-130. doi:10.1016/0021-9045(90)90028-o

Repository Citation

Swetits, J. J. and Weinstein, S. E., "Construction of the Best Monotone Approximation on Lp [0, 1]" (1990). Mathematics & Statistics Faculty Publications. 112.
https://digitalcommons.odu.edu/mathstat_fac_pubs/112