Almost exactness in normed spaces II

Saturating Constructions for Normed Spaces II

We prove several results of the following type: given finite dimensional normed space V possessing certain geometric property there exists another space X having the same property and such that (1) log dimX = O(log dimV ) and (2) every subspace of X, whose dimension is not “too small,” contains a further wellcomplemented subspace nearly isometric to V . This sheds new light on the structure of ...

-approximation in normed spaces

Differentiable Functions on Normed Linear Spaces. Part II

The terminology and notation used in this paper have been introduced in the following articles: [16], [3], [19], [5], [4], [1], [15], [6], [17], [18], [9], [8], [2], [20], [12], [14], [10], [13], [7], and [11]. For simplicity, we adopt the following rules: S, T denote non trivial real normed spaces, x0 denotes a point of S, f denotes a partial function from S to T , h denotes a convergent to 0 ...

BEST SIMULTANEOUS APPROXIMATION IN FUZZY NORMED SPACES

The main purpose of this paper is to consider the t-best simultaneousapproximation in fuzzy normed spaces. We develop the theory of t-bestsimultaneous approximation in quotient spaces. Then, we discuss the relationshipin t-proximinality and t-Chebyshevity of a given space and its quotientspace.

t-BEST APPROXIMATION IN FUZZY NORMED SPACES

The main purpose of this paper is to find t-best approximations in fuzzy normed spaces. We introduce the notions of t-proximinal sets and F-approximations and prove some interesting theorems. In particular, we investigate the set of all t-best approximations to an element from a set.