scholarly journals Homeomorphisms group of normed vector space: Conjugacy problems and the Koopman operator

2013 ◽  
Vol 33 (9) ◽  
pp. 3957-3980 ◽  
Author(s):  
Mickaël D. Chekroun ◽  
◽  
Jean Roux ◽  
Keyword(s):  
Vector Space ◽  
Normed Vector Space ◽  
Koopman Operator ◽  
Normed Vector

The M-Space Theory of Tolerances

1990 ◽  
Author(s):  
Joshua U. Turner ◽  
Michael J. Wozny
Keyword(s):  
Vector Space ◽  
Mathematical Theory ◽  
Solid Modeling ◽  
Normed Vector Space ◽  
Space Theory ◽  
Modeling Technology ◽  
Geometric Tolerances ◽  
Normed Vector

Abstract A rigorous mathematical theory of tolerances is an important step toward the automated solution of tolerancing problems. This paper develops a mathematical theory of tolerances in which tolerance specifications are interpreted as constraints on a normed vector space of model variations (M-space). This M-space provides concise representations for both dimensional and geometric tolerances, without deviating from the established tolerancing standards. This paper extends the authors’ previous work to include examples of geometric orientation and form tolerances. We show that the M-space theory supports the development of effective algorithms for the solution of tolerancing problems. Through the use of solid modeling technology, it is possible to automate the solution of such problems.

scholarly journals On the stability of radical septic functional equations

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2229
Author(s):  
Emanuel Guariglia ◽  
Kandhasamy Tamilvanan
Keyword(s):  
Functional Equation ◽  
Approximate Solution ◽  
Vector Space ◽  
Banach Spaces ◽  
Functional Equations ◽  
Normed Vector Space ◽  
Relevant Case ◽  
The Stability ◽  
Normed Vector ◽  
Stability Results

This paper deals with the approximate solution of the following functional equation fx7+y77=f(x)+f(y), where f is a mapping from R into a normed vector space. We show stability results of this equation in quasi-β-Banach spaces and (β,p)-Banach spaces. We also prove the nonstability of the previous functional equation in a relevant case.

scholarly journals Two fixed point theorems and invariant integrals

1974 ◽  
Vol 11 (1) ◽  
pp. 15-30 ◽  
Author(s):  
T.J. Cooper ◽  
J.H. Michael
Keyword(s):  
Fixed Point ◽  
Vector Space ◽  
Fixed Point Theorems ◽  
Normed Vector Space ◽  
Invariant Integrals ◽  
Lower Semi ◽  
Normed Vector

Two fixed point theorems for a subset C of a normed vector space X are established by using the concept of centre. These results differ from previous fixed point theorems in that X is assumed to have a topology T as well as a norm. The norm is required to be lower semi-continuous with respect to T and C is required to be convex, bounded with respect to the norm and compact with respect to T.

Uniform Domains and Uniform Domain Decomposition Property in Real Normed Vector Spaces

2013 ◽  
Vol 113 (1) ◽  
pp. 128 ◽  
Author(s):  
M. Huang ◽  
X. Wang
Keyword(s):  
Vector Space ◽  
Domain Decomposition ◽  
Vector Spaces ◽  
Uniform Domain ◽  
Normed Vector Space ◽  
Decomposition Property ◽  
Uniform Domains ◽  
Normed Vector

Let $E$ be a real normed vector space with $\dim(E)\geq 2$, $D$ a proper subdomain of $E$. In this paper we characterize uniform domains in $E$ in terms of the uniform domain decomposition property. In addition, we discuss the relation between quasiballs and domains with the quasiball decomposition property in $\mathsf{R}^n$.

Measures under the flat norm as ordered normed vector space

Positivity ◽  
2017 ◽  
Vol 22 (1) ◽  
pp. 105-138
Author(s):  
Piotr Gwiazda ◽  
Anna Marciniak-Czochra ◽  
Horst R. Thieme
Keyword(s):  
Vector Space ◽  
Normed Vector Space ◽  
Flat Norm ◽  
Normed Vector

scholarly journals The Joly topology and the Mosco-Beer topology revisited

1993 ◽  
Vol 48 (3) ◽  
pp. 353-363 ◽  
Author(s):  
Dominique Azé ◽  
Jean-Paul Penot
Keyword(s):  
Vector Space ◽  
Convex Functions ◽  
Normed Vector Space ◽  
Fenchel Transform ◽  
Proper Convex ◽  
Normed Vector

Some extensions to the non reflexive case of continuity results for the Legendre-Fenchel transform are presented following an approach due to J.-L. Joly. We compare the topology introduced by J.-L. Joly and the Mosco-Beer topology introduced by G. Beer. In particular, in the case of the space of closed proper convex functions defined on the dual of a normed vector space they coincide.

scholarly journals A remark on continuous bilinear mappings

1971 ◽  
Vol 17 (3) ◽  
pp. 245-248 ◽  
Author(s):  
J. W. Baker ◽  
J. S. Pym
Keyword(s):  
Vector Space ◽  
Banach Algebra ◽  
Dimensional Subspace ◽  
Real Field ◽  
Normed Vector Space ◽  
Normed Algebra ◽  
One Dimensional ◽  
Bilinear Mapping ◽  
Second Dual ◽  
Normed Vector

The main theorem of this paper is a little involved (though the proof is straightforward using a well-known idea) but the immediate corollaries are interesting. For example, take a complex normed vector space A which is also a normed algebra with identity under each of two multiplications * and ∘. Then these multiplications coincide if and only if there exists α such that ‖a ∘ b ‖ ≦ α ‖ a * b ‖ for a, b in A. This is a condition for the two Arens multiplications on the second dual of a Banach algebra to be identical. By taking * to be the multiplication of a Banach algebra and ∘ to be its opposite, we obtain the condition for commutativity given in (3). Other applications are concerned with conditions under which a bilinear mapping between two algebras is a homomorphism, when an element lies in the centre of an algebra, and a one-dimensional subspace of an algebra is a right ideal. An example shows that the theorem is false for algebras over the real field, but Theorem 2 gives the parallel result in this case.

scholarly journals Correction to: Measures under the flat norm as ordered normed vector space

Positivity ◽  
2017 ◽  
Vol 22 (1) ◽  
pp. 139-140 ◽  
Author(s):  
Piotr Gwiazda ◽  
Anna Marciniak-Czochra ◽  
Horst R. Thieme
Keyword(s):  
Vector Space ◽  
Normed Vector Space ◽  
Flat Norm ◽  
Normed Vector

scholarly journals On differentiability of mappings with finite dilation

2015 ◽  
Vol 62 (1) ◽  
pp. 133-141
Author(s):  
Małgorzata Turowska
Keyword(s):  
Vector Space ◽  
Lipschitz Mapping ◽  
Normed Vector Space ◽  
Almost Everywhere ◽  
Normed Vector

Abstract We study mappings f : (a,b) → Y with finite dilation having Lebesgue integrable majorant, where Y is a real normed vector space. We construct Lipschitz mapping f : (a,b) → Y, dim Y = ∞ , which is nowhere differentiable but its graph has everywhere trivial contingent. We show that if the contingent of the graph of a mapping with finite dilation is a nontrivial space, then f is almost everywhere differentiable.

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