A Duality Approach to Best Uniform Convex Approximation

Authors

S. E. Weinstein, Old Dominion University
Yuesheng Xu, Old Dominion University

Document Type

Article

Publication Date

1991

DOI

10.1016/0022-247x(91)90308-m

Publication Title

Journal of Mathematical Analysis and Applications

Volume

160

Issue

2

Pages

314-322

Abstract

Let C[a, b] be the space of continuous functions on [a, b] endowed with the uniform norm llƒll _∞ = sup{ Iƒ(x)1 :x∈ [a, b]}. Let K be the set of convex functions defined on [a, b]. A function g* ∈ K is said to be a best uniform convex approximation to ƒ ∈ C[a, b] if ∥ƒ - g*∥ _∞ = inf { ∥ƒ - g∥_∞ : g ∈ K}.

Comments

Elsevier open archive. Copyright © 1991 Published by Elsevier Inc. All rights reserved.

Original Publication Citation

Weinstein, S. E., & Xu, Y. S. (1991). A duality approach to best uniform convex approximation. Journal of Mathematical Analysis and Applications, 160(2), 314-322. doi:10.1016/0022-247x(91)90308-m

Repository Citation

Weinstein, S. E. and Xu, Yuesheng, "A Duality Approach to Best Uniform Convex Approximation" (1991). Mathematics & Statistics Faculty Publications. 119.
https://digitalcommons.odu.edu/mathstat_fac_pubs/119