journal6 ›› 2006, Vol. 27 ›› Issue (3): 1-3.

• Mathematics •     Next Articles

Uniqueness of Approximation in Lp(μ,X)


  1. (College of Mathematics and Computer Science,Jishou University,Jishou  416000,Hunan China)
  • Online:2006-05-25 Published:2012-09-11

Abstract: Let X be a Banach space and Y a closed convex subset of X containing the original.The following is the main result of this paper:Lp(μ,Y) is a Chebyshev subset of Lp(μ,X) (1<p<∞) if and only if L1(μ,Y) is a Chebyshev subset of L1(μ,X).In addition,this paper gives an example to show that the conclusion “that g is a best approximation to f∈L∞(μ,X) from L∞(μ,Y) implies g(s)∈ PY(f(s)) for almost all s∈Ω” is not true.

Key words: best approximation, Chebyshev subset, closed convex set

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