scholarly journals New Characterization for Nonlinear Weighted Best Simultaneous Approximation

2009 ◽  
Vol 2009 ◽  
pp. 1-9
Author(s):  
Xianfa Luo ◽  
Delin Wu ◽  
Jinsu He
Keyword(s):  
Wide Class ◽  
Simultaneous Approximation ◽  
Regular Point ◽  
Linear Spaces ◽  
Characterization Result ◽  
Normed Linear Spaces ◽  
Best Simultaneous Approximation

This paper is concerned with the problem of a wide class of weighted best simultaneous approximation in normed linear spaces, and it establishes a new characterization result for the class of approximation by virtue of the notion of simultaneous regular point.

On Best Simultaneous Approximation in Normed Linear Spaces

1974 ◽  
Vol 17 (4) ◽  
pp. 523-527 ◽  
Author(s):  
D. S. Goel ◽  
A. S. B. Holland ◽  
C. Nasim ◽  
B. N. Sahney
Keyword(s):  
Simultaneous Approximation ◽  
Continuous Functions ◽  
Supremum Norm ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Best Simultaneous Approximation ◽  
Image Position

Let S be a non-empty family of real valued continuous functions on [a, b]. Diaz and McLaughlin [1], [2], and Dunham [3] have considered the problem of simultaneously approximating two continuous functions f1 and f2 by elements of S. If || • || denotes the supremum norm, then the problem is to find an element * ∈ S if it exists, for which

A Note on Best Simultaneous Approximation in Normed Linear Spaces

1976 ◽  
Vol 19 (3) ◽  
pp. 359-360 ◽  
Author(s):  
Arne Brøndsted
Keyword(s):  
Linear Space ◽  
Convex Subset ◽  
Convex Functions ◽  
Existence And Uniqueness ◽  
Simultaneous Approximation ◽  
Normed Linear Space ◽  
Present Note ◽  
Linear Spaces ◽  
Best Simultaneous Approximation ◽  
Image Position

The purpose of the present note is to point out that the results of D. S. Goel, A. S. B. Holland, C. Nasim and B. N. Sahney [1] on best simultaneous approximation are easy consequences of simple facts about convex functions. Given a normed linear space X, a convex subset K of X, and points x1, x2 in X, [1] discusses existence and uniqueness of K* ∈ K such that

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