Finite dimensional fuzzy normed linear space

1992 ◽  
Vol 48 (2) ◽  
pp. 239-248 ◽  
Author(s):  
Clementina Felbin
Keyword(s):  
Linear Space ◽  
Normed Linear Space ◽  
Finite Dimensional

scholarly journals Auerbach Bases and Minimal Volume Sufficient Enlargements

2011 ◽  
Vol 54 (4) ◽  
pp. 726-738
Author(s):  
M. I. Ostrovskii
Keyword(s):  
Linear Space ◽  
Isometric Embedding ◽  
Normed Linear Space ◽  
Convex Set ◽  
Linear Projection ◽  
Minimal Volume ◽  
Finite Dimensional ◽  
Dimensional Normed Space ◽  
Closed Convex Set

AbstractLet BY denote the unit ball of a normed linear space Y. A symmetric, bounded, closed, convex set A in a finite dimensional normed linear space X is called a sufficient enlargement for X if, for an arbitrary isometric embedding of X into a Banach space Y, there exists a linear projection P: Y → X such that P(BY ) ⊂ A. Each finite dimensional normed space has a minimal-volume sufficient enlargement that is a parallelepiped; some spaces have “exotic” minimal-volume sufficient enlargements. The main result of the paper is a characterization of spaces having “exotic” minimal-volume sufficient enlargements in terms of Auerbach bases.

scholarly journals Some results on finite dimensional fuzzy cone normed linear space

2017 ◽  
Vol 13 (1) ◽  
pp. 123-134 ◽  
Author(s):  
P. Tamang ◽  
T. Bag
Keyword(s):  
Linear Space ◽  
Normed Linear Space ◽  
Finite Dimensional

scholarly journals Finite Dimensional Chebyshev Subspaces of Lo

2017 ◽  
Vol 22 (1) ◽  
pp. 53
Author(s):  
Aref K. Kamal
Keyword(s):  
Linear Space ◽  
Best Approximation ◽  
Normed Linear Space ◽  
The Best Approximation ◽  
Finite Dimensional

If A is a subset of the normed linear space X, then A is said to be proximinal in X if for each xÎX there is a point y0ÎA such that the distance between x and A; d(x, A) = inf{||x-y||: yÎA}= ||x­-y0||. The element y0 is called a best approximation for x from A. If for each xÎX, the best approximation for x from A is unique then the subset A is called a Chebyshev subset of X.  In this paper the author studies the existence of finite dimensional Chebyshev subspaces of Lo.   

On the existence of support maps with dense images

1977 ◽  
Vol 23 (4) ◽  
pp. 504-510
Author(s):  
Brailey Sims
Keyword(s):  
Linear Space ◽  
Normed Linear Space ◽  
Dense Subset ◽  
Sufficient Conditions ◽  
Complete Answer ◽  
Finite Dimensional

AbstractFor a normed linear space X we investigate conditions for the existence of support maps under which the image of X is a dense subset of the dual. In the case of finite-dimensional spaces a complete answer is given. For more general spaces some sufficient conditions are obtained.

scholarly journals The L1-version of the Diliberto–Straus algorithm in C(T × S)

1984 ◽  
Vol 27 (1) ◽  
pp. 31-45 ◽  
Author(s):  
W. A. Light ◽  
S. M. Holland
Keyword(s):  
Linear Space ◽  
Best Approximation ◽  
Measure Space ◽  
Normed Linear Space ◽  
Finite Measure ◽  
Hausdorff Spaces ◽  
Chebyshev Subspace ◽  
Borel Measures ◽  
Finite Dimensional ◽  
Measure Spaces

Let (S, Σ, μ) and (T, Θ, v) be two measure spaces of finite measure where we assume S, T are compact Hausdorff spaces and μ, v are regular Borel measures. We construct the product measure space (T x S, >, Φ σ) in the usual way. Let G = [gl, g2, …, gp] and H = [hl, h1, …, hm be finite dimensional subspaces of C(S) and C(T) respectivelywhere G and H are also Chebyshev with respect to the L1-norm. Note that a subspace Y of a normed linear space X is Chebyshev if each x ∈X possesses exactly one best approximation y ∈Y. For example, in C(S) with the L1-norm, the subspace of polynomials of degree at most n is a Chebyshev subspace. This is an old theorem of Jackson. Now set

scholarly journals Convex sets in proximal relator spaces

Filomat ◽  
2016 ◽  
Vol 30 (13) ◽  
pp. 3411-3414 ◽  
Author(s):  
J.F. Peters
Keyword(s):  
Linear Space ◽  
Normed Linear Space ◽  
Convex Sets ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Finite Dimensional

This article introduces convex sets in finite-dimensional normed linear spaces equipped with a proximal relator. A proximal relator is a nonvoid family of proximity relations R? (called a proximal relator) on a nonempty set. A normed linear space endowed with R? is an extension of the Sz?z relator space. This leads to a basis for the study of the nearness of convex sets in proximal linear spaces.

Weak Cauchy sequences in normed linear spaces

1964 ◽  
Vol 60 (4) ◽  
pp. 817-819 ◽  
Author(s):  
D. J. H. Garling
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Linear Space ◽  
Cauchy Sequence ◽  
Normed Linear Space ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Finite Dimensional ◽  
Cauchy Sequences ◽  
Convex Cover

It follows from the Krein-Milman theorem that (c0) is not isomorphic to the dual of a Banach space. Using a technique due to Banach ((4), page 194) we shall extend this result to show that if a subspace of (c0) is isomorphic to the dual of a normed linear space, then it is finite dimensional (Proposition 1). Using this result, we shall show that if E is a normed linear space, the unit ball of which is contained in the closed absolutely convex cover of a weak Cauchy sequence, then Eis finite dimensional (Proposition 2). This result has applications to the Banach-Dieudonné theorem, and to the theory of two-norm spaces.

scholarly journals Fixed points of quasi-nonexpansive mappings

1972 ◽  
Vol 13 (2) ◽  
pp. 167-170 ◽  
Author(s):  
W. G. Dotson
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Linear Space ◽  
Complex Plane ◽  
Normed Linear Space ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
The Other ◽  
Commuting Mappings ◽  
Analytic Mappings

A self-mapping T of a subset C of a normed linear space is said to be non-expansive provided ║Tx — Ty║ ≦ ║x – y║ holds for all x, y ∈ C. There has been a number of recent results on common fixed points of commutative families of nonexpansive mappings in Banach spaces, for example see DeMarr [6], Browder [3], and Belluce and Kirk [1], [2]. There have also been several recent results concerning common fixed points of two commuting mappings, one of which satisfies some condition like nonexpansiveness while the other is only continuous, for example see DeMarr [5], Jungck [8], Singh [11], [12], and Cano [4]. These results, with the exception of Cano's, have been confined to mappings from the reals to the reals. Some recent results on common fixed points of commuting analytic mappings in the complex plane have also been obtained, for example see Singh [13] and Shields [10].

Convex Functions on a Normed Linear Space

2006 ◽  
pp. 101-176
Author(s):  
Constantin P. Niculescu ◽  
Lars-Erik Persson
Keyword(s):  
Linear Space ◽  
Convex Functions ◽  
Normed Linear Space
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