Dependence on p of the best Lp approximation operator

Some Results on p-Best Approximation in Vector Spaces

Best Basis Selection for Approximation in Lp

We study the approximation of a function class F in Lp by choosing first a basis B and then using n-term approximation with the elements of B. Into the competition for best bases we enter all greedy (i.e. democratic and unconditional [20]) bases for Lp. We show that if the function class F is well oriented with respect to a particular basis B then, in a certain sense, this basis is the best cho...

Best Simultaneous Approximation in Lp(I, E)

Let G be a reflexive subspace of the Banach space E and let L(I, E) denote the space of all p-Bochner integrable functions on the interval I=[0, 1] with values in E, 1 [ pO.. Given any norm N(· , · ) on R, N nondecreasing in each coordinate on the set R +, we prove that L (I, G) is N-simultaneously proximinal in L(I, E). Other results are also obtained. © 2002 Elsevier Science (USA)

Asymptotic expression of the linear discrete best lp-approximation

Let hp , 1 1, where p ∈ Rn with ‖ p‖ = o ( ap/p ) . © 2006 Elsevier Inc. All rights reserved.

some results on p-best approximation in vector spaces