Best Simultaneous Local Approximation in the Lp Norms. (3rd June 2017)

• Record Type: Journal Article
• Authors: Ferreyra, D. E.; Levis, F. E.
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 6(2017)
• Page Start: 770
• Page End: 798
• Publication Date: 2017-06-03
• Subjects: Convex sets -- Lp spaces -- simultaneous approximation; 41A28 -- 41A10; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1291520
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: We study the behavior of the best simultaneous approximation to two functions from a convex set in L p spaces, 2< p <∞, on a finite union of intervals when its measure tends to zero. In particular, we give sufficient conditions over the differentiability of two functions to assure existence of the best simultaneous local approximation from the class of algebraic polynomials of a fixed degree. These conditions are weaker than the ordinary differentiability given in previous works. More precisely, we consider differentiable functions in the sense L p .