Best simultaneous approximation of bounded functions with values in certain Banach spaces

1979 ◽  
Vol 240 (2) ◽  
pp. 157-164 ◽  
Author(s):  
Jaroslav Mach
Keyword(s):  
Banach Spaces ◽  
Simultaneous Approximation ◽  
Bounded Functions ◽  
Best Simultaneous Approximation

scholarly journals Best Simultaneous Approximation in Orlicz Spaces

2007 ◽  
Vol 2007 ◽  
pp. 1-7 ◽  
Author(s):  
M. Khandaqji ◽  
Sh. Al-Sharif
Keyword(s):  
Banach Space ◽  
Simultaneous Approximation ◽  
Closed Subspace ◽  
Orlicz Spaces ◽  
Unit Interval ◽  
Luxemburg Norm ◽  
Integrable Functions ◽  
Best Simultaneous Approximation ◽  
Distance Formula

LetXbe a Banach space and letLΦ(I,X)denote the space of OrliczX-valued integrable functions on the unit intervalIequipped with the Luxemburg norm. In this paper, we present a distance formula dist(f1,f2,LΦ(I,G))Φ, whereGis a closed subspace ofX, andf1,f2∈LΦ(I,X). Moreover, some related results concerning best simultaneous approximation inLΦ(I,X)are presented.

scholarly journals Best Simultaneous approximation of quasi-continuous functions by monotone functions

1991 ◽  
Vol 50 (3) ◽  
pp. 391-408 ◽  
Author(s):  
Salem M. A. Sahab
Keyword(s):  
Banach Space ◽  
Convex Cone ◽  
Simultaneous Approximation ◽  
Continuous Functions ◽  
Unit Interval ◽  
Closed Convex Cone ◽  
Monotone Functions ◽  
Measurable Functions ◽  
Best Simultaneous Approximation ◽  
Nondecreasing Functions

AbstractLet 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∞.

scholarly journals On best simultaneous approximation

1976 ◽  
Vol 17 (2) ◽  
pp. 187-188 ◽  
Author(s):  
A.S.B Holland ◽  
B.N Sahney ◽  
J Tzimbalario
Keyword(s):  
Simultaneous Approximation ◽  
Best Simultaneous Approximation

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.

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