Let X be a normed linear space. We will consider only normed linear spaces over R (Real line), though many of the results we describe hold good for n.l. spaces over C (the complex plane). The dual of X, the class of all bounded, linear functionals on X, is denoted by X∗. The closed unit ball of X is denoted by BX and the unit sphere, by SX . That is, BX = {x ∈ X : ‖x‖ ≤ 1} and SX = {x ∈ X : ‖x‖...

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)

A closed subspace M in a Banach space X is called t/-proximinal if it satisfies: (1 + p)S n (S + M) ç S + e(pXS n M), for some positive valued function t(p), p > 0, and e(p) -» 0 as p -> 0, where 5 is the closed unit ball of X. One of the important properties of this class of subspaces is that the metric projections are continuous. We show that many interesting subspaces are (/-proximinal, for ...

We characterize finite-dimensional normed linear spaces as strongly proximinal subspaces in all their superspaces. A connection between upper Hausdorff semi-continuity of metric projection and finite dimensionality of subspace is given.

The main purpose of this paper, is to investigate the basic properties of t-proximinal sets. At first we prove some main results and then we see some classified cases, in finite dimensional fuzzy normed spaces.