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.

This paper is concerned with the problem of nonlinear best simultaneous approximations in K?the Bochner function spaces respect to Minkowski? norms Euclidean spaces. Characterization results generalized approximation are established. These considered a generalization concerning Lebesgue and Orlicz

We investigate the problem of best simultaneous Diophantine approximation under a constraint on the denominator, as proposed by Jurkat. New lower estimates for optimal approximation constants are given in terms of critical determinants of suitable star bodies. Tools are results on simultaneous Diophantine approximation of rationals by rationals with smaller denominator. Finally, the approximati...

The present paper is concerned with the problem of weighted best simultaneous approximations in Banach spaces. The weighted best simultaneous approximations to sequences from Sand BS-suns in the Banach space are characterized in view of the Kolmogorov conditions. Applications are provided for weighted best simultaneous approximations from RS-sets and strict RS-sets. Our results obtained in the ...

We study the behavior of best simultaneous (lq , Lp)-approximation by rational functions on an interval, when the measure tends to zero. In addition, we consider the case of polynomial approximation on a finite union of intervals. We also get an interpolation result.

Recommended by Ricardo Estrada Let X be a Banach space and let L Φ (I,X) denote the space of Orlicz X-valued integrable functions on the unit interval I equipped with the Luxemburg norm. In this paper, we present a distance formula dist Φ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in a...

The problem of best simultaneous approximation has a long history and continues to generate much interest. The problem of approximating simultaneously two continuous functions on a finite closed interval was first studied by Dunham 1 . Since then, such problems have been extended extensively, see, for example, 1–7 and references therein. In particular, characterization and uniqueness results we...