In this survey, the notion of a balanced best multipoint local approximation is fully exposed since they were treated in the Lp spaces and recent results in Orlicz spaces. The notion of balanced point, which was introduced ...

The best polynomial approximation operator was recently extended by one of the authors from Lp to Lp−1. In this paper, we study weak and strong inequalities for maximal operators related with the extended best polynomial ...

In this paper we study the behavior of best Lp-approximations by rational functions to an analytic function on union of disks, when the measure of them tends to zero.

In this paper, we extend results given by Z´o and Cuenya in 2007 about a general approach to problems of best vector-valued approximation on small regions from a finite dimensional subspace of polynomials of some degree. ...

Given an Orlicz space Lφ, we give very relaxed sufficient conditions on φ to ensure that there exists a best φ-approximation from any finite dimensional bounded linear subspace S ⊂ Lφ. In addition, given an operator T, ...

We present a common fixed point theorem for generalized asymptotically nonexpansive and noncommuting mappings in normed linear spaces.

Given an non necessarily linear operator T defined from an Orlicz space L φ′(Ω, , μ) into itself, where φ′ denote the derivative of a strictly convex function φ, we give necessary and sufficient conditions on T assuring ...

In this article we consider the best polynomial approximation operator, defined in an Orlicz space L Φ(B), and its extension to L ϕ(B) where ϕ is the derivative function of Φ. A characterization of these operators and ...

In this paper we study a maximal operator Mf related with the best ϕ approximation by constants for a function f ∈ L ϕ 0 loc(ℝn), where we denote by ϕ 0 for the derivative function of the C1 convex function ϕ. We get a ...

In this short note, we show the behavior in Orlicz spaces of best approximations by algebraic polynomials pairs on union of neighborhoods, when the measure of them tends to zero.