On some Lp inequalities in best approximation theory

Some Results on p-Best Approximation in Vector Spaces

On Maximal Inequalities Arising in Best Approximation

Let f be a function in an Orlicz space L and μ(f,L) be the set of all the best Φ-approximants to f, given a σ−lattice L. Weak type inequalities are proved for the maximal operator f∗ = supn |fn|, where fn is any selection of functions in μ(f,Ln), and Ln is an increasing sequence of σ-lattices. Strong inequalities are proved in an abstract set up which can be used for an operator as f∗.

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)

Best Approximation in TVS

In this paper  we give newresults on the best approximation  in the Hausdorff topological vectorspace and  consider relationship  with orthogonality. Also we determined under  what conditions the map $P_{K,f}$ is upper semicontinous.