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 ...

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. ...

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

We introduce a concept of best local approximation using abstract norms and non-homogeneous dilations. The asymptotic behavior of the normalized error function as well as the limit of some net of best approximation polynomials ...

In this article, we introduce the τ condition, which is weaker than the L2 differentiability. If a function satisfies the τ condition on two points of, we prove the existence and characterization of the best local polynomial ...

In this paper we prove the existence of best multipoint local ||·||−approximation to a function f from an N−dimensional space SN for a suitable integer N. This problem is considered in an arbitrary Orlicz space for both ...

We introduce two classes of functions, one containing the classof L2 differentiable functions, and another containing the class of L2 lateraldifferentiable functions. For functions in these new classes we prove existenceof ...

In this short note, we study inequalities for algebraic polynomials on measurable sets in Lorentz spaces and discuss their applications to best approximation.

We study the convergence of a net of subspaces generated by dilations of polynomials in a finite dimensional subspace. As a consequence, we extend the results given by Z´o and Cuenya [Advanced Courses of Mathematical ...

We study the behavior of the best simultaneous approximation to two functions from a convex set in Lp spaces, 2<p<∞, on a finite union of intervals when its measure tends to zero. In particular, we give sufficient conditions ...