Antiproximinal sets in the Banach space c(X)c(X)

summary:If $X$ is a Banach space then the Banach space $c(X)$ of all $X$-valued convergent sequences contains a nonvoid bounded closed convex body $V$ such that no point in $C(X)\setminus V$ has a nearest point in $V$

Note on the paper of I. Muntean ''On the method of near equations''

Not available

Compactness in spaces of Lipschitz functions

The aim of this paper is to prove a compactness criterium in spaces of Lipschitz and Frechet dierentiable mappings

Extension of bounded linear functionals and best approximation in spaces with asymmetric norm

The present paper is concerned with the characterization of the elements of best approximation in a subspace $Y$ of a space with asymmetric norm, in terms of some linear functionals vanishing on $Y$. The approach is based on some extension results, proved in Section 3, for bounded linear functionals on such spaces. Also, the well known formula for the distance to a hyperplane in a normed space is extended to the nonsymmetric case