scholarly journals Finite dimensional characteristics related to superreflexivity of Banach spaces

2004 ◽  
Vol 69 (2) ◽  
pp. 289-295 ◽  
Author(s):  
M. I. Ostrovskii
Keyword(s):  
Banach Spaces ◽  
Normed Space ◽  
Local Theory ◽  
Normed Spaces ◽  
Finite Sets ◽  
Large Cardinality ◽  
Finite Dimensional ◽  
Finite Set

One of the important problems of the local theory of Banach Spaces can be stated in the following way. We consider a condition on finite sets in normed spaces that makes sense for a finite set any cardinality. Suppose that the condition is such that to each set satisfying it there corresponds a constant describing “how well” the set satisfies the condition.The problem is:Suppose that a normed space X has a set of large cardinality satisfying the condition with “poor” constant. Does there exist in X a set of smaller cardinality satisfying the condition with a better constant?In the paper this problem is studied for conditions associated with one of R.C. James's characterisations of superreflexivity.

scholarly journals Some fixed point theorems in n-normed spaces

2020 ◽  
Vol 25 (3) ◽  
pp. 1-15 ◽  
Author(s):  
Hanan Sabah Lazam ◽  
Salwa Salman Abed
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Normed Space ◽  
Fixed Point Theorems ◽  
Normed Spaces ◽  
Weak Contraction ◽  
Contraction Mappings ◽  
Basic Properties ◽  
Definition Of

In this article, we recall the definition of a real n-normed space and some basic properties. fixed point theorems for types of Kannan, Chatterge, Zamfirescu, -Weak contraction and  - (,)-Weak contraction mappings in  Banach spaces.

scholarly journals Onn-normed spaces

2001 ◽  
Vol 27 (10) ◽  
pp. 631-639 ◽  
Author(s):  
Hendra Gunawan ◽  
M. Mashadi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Normed Space ◽  
Normed Spaces

Given ann-normed space withn≥2, we offer a simple way to derive an(n−1)-norm from then-norm and realize that anyn-normed space is an(n−1)-normed space. We also show that, in certain cases, the(n−1)-norm can be derived from then-norm in such a way that the convergence and completeness in then-norm is equivalent to those in the derived(n−1)-norm. Using this fact, we prove a fixed point theorem for somen-Banach spaces.

scholarly journals The horofunction boundary of finite-dimensional normed spaces

2007 ◽  
Vol 142 (3) ◽  
pp. 497-507 ◽  
Author(s):  
CORMAC WALSH
Keyword(s):  
Unit Ball ◽  
Normed Space ◽  
Normed Spaces ◽  
Finite Dimensional ◽  
Dimensional Normed Space

AbstractWe determine the set of Busemann points of an arbitrary finite-dimensional normed space. These are the points of the horofunction boundary that are the limits of “almost-geodesics”. We prove that all points in the horofunction boundary are Busemann points if and only if the set of extreme sets of the dual unit ball is closed in the Painlevé–Kuratowski topology.

scholarly journals Maximum average distance in complex finite dimensional normed spaces

2002 ◽  
Vol 66 (1) ◽  
pp. 125-134
Author(s):  
Juan C. García-Vázquez ◽  
Rafael Villa
Keyword(s):  
Unit Sphere ◽  
Metric Space ◽  
Normed Space ◽  
Average Distance ◽  
Complex Case ◽  
Normed Spaces ◽  
Finite Dimensional ◽  
Real Normed Space ◽  
Dimensional Normed Space

A number r > 0 is called a rendezvous number for a metric space (M, d) if for any n ∈ ℕ and any x1,…xn ∈ M, there exists x ∈ M such that . A rendezvous number for a normed space X is a rendezvous number for its unit sphere. A surprising theorem due to O. Gross states that every finite dimensional normed space has one and only one average number, denoted by r (X). In a recent paper, A. Hinrichs solves a conjecture raised by R. Wolf. He proves that for any n-dimensional real normed space. In this paper, we prove the analogous inequality in the complex case for n ≥ 3.

scholarly journals A Shrinking Projection Algorithm with Errors for Costerro Bounded Linear Mappings

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Joseph Frank Gordon
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Projection Algorithm ◽  
Uniformly Convex ◽  
Bounded Linear ◽  
Finite Dimensional ◽  
Finite Set ◽  
Shrinking Projection Algorithm

The purpose of this paper is to introduce and analyze the shrinking projection algorithm with errors for a finite set of costerro bounded linear mappings in the setting of uniformly convex smooth Banach spaces. Here, under finite dimensional or compactness restriction or the error term being zero, the strong limit point of the sequence stated in the iterative scheme for these mappings in uniformly convex smooth Banach spaces was studied. This paper extends Ezearn and Prempeh’s result for nonexpansive mappings in real Hilbert spaces.

scholarly journals Connections Between the Completion of Normed Spaces Over Non-Archimedean Fields and the Stability of the Cauchy Equation

2020 ◽  
Vol 34 (1) ◽  
pp. 151-163
Author(s):  
Jens Schwaiger
Keyword(s):  
Banach Spaces ◽  
Normed Space ◽  
Close Connection ◽  
Normed Spaces ◽  
Cauchy Equation ◽  
Absolute Value ◽  
Pexider Equation ◽  
Adic Valuation ◽  
The Stability ◽  
Stability Results

AbstractIn [12] a close connection between stability results for the Cauchy equation and the completion of a normed space over the rationals endowed with the usual absolute value has been investigated. Here similar results are presented when the valuation of the rationals is a p-adic valuation. Moreover a result by Zygfryd Kominek ([5]) on the stability of the Pexider equation is formulated and proved in the context of Banach spaces over the field of p-adic numbers.

On I-convergence in random 2-normed spaces

2011 ◽  
Vol 61 (6) ◽  
Author(s):  
M. Mursaleen ◽  
Abdullah Alotaibi
Keyword(s):  
Banach Spaces ◽  
Normed Space ◽  
Statistical Convergence ◽  
Normed Spaces ◽  
Ideal Convergence

AbstractRecently the concepts of statistical convergence and ideal convergence have been studied in 2-normed and 2-Banach spaces by various authors. In this paper we define and study the notion of ideal convergence in random 2-normed space and construct some interesting examples.

Another approach to characterizations of generalized triangle inequalities in normed spaces

2014 ◽  
Vol 12 (11) ◽  
Author(s):  
Tamotsu Izumida ◽  
Ken-Ichi Mitani ◽  
Kichi-Suke Saito
Keyword(s):  
Banach Spaces ◽  
Normed Space ◽  
Triangle Inequality ◽  
Normed Spaces ◽  
Direct Sums ◽  
Nonlinear Anal ◽  
Generalized Triangle Inequality

AbstractIn this paper, we consider a generalized triangle inequality of the following type: $$\left\| {x_1 + \cdots + x_n } \right\|^p \leqslant \frac{{\left\| {x_1 } \right\|^p }} {{\mu _1 }} + \cdots + \frac{{\left\| {x_2 } \right\|^p }} {{\mu _n }}\left( {for all x_1 , \ldots ,x_n \in X} \right),$$ where (X, ‖·‖) is a normed space, (µ1, ..., µn) ∈ ℝn and p > 0. By using ψ-direct sums of Banach spaces, we present another approach to characterizations of the above inequality which is given by [Dadipour F., Moslehian M.S., Rassias J.M., Takahasi S.-E., Nonlinear Anal., 2012, 75(2), 735–741].

scholarly journals On products of idempotent matrices

1967 ◽  
Vol 8 (2) ◽  
pp. 118-122 ◽  
Author(s):  
J. A. Erdos
Keyword(s):  
Vector Spaces ◽  
Dimensional Vector ◽  
Finite Sets ◽  
Linear Transformations ◽  
Proved Theorem ◽  
Finite Dimensional ◽  
Finite Set ◽  
Semigroup Of Transformations

In [1], J. M. Howie considered the semigroup of transformations of sets and proved (Theorem 1) that every transformation of a finite set which is not a permutation can be written as a product of idempotents. In view of the analogy between the theories of transformations of finite sets and linear transformations of finite dimensional vector spaces, Howie's theorem suggests a corresponding result for matrices. The purpose of this note is to prove such a result.

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