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1
Content available remote

Examples of sequential topological groups under the continuum hypothesis

100%
Shibakov A.
Fundamenta Mathematicae
|
1996
|
tom 151
|
nr 2
107-120
EN
Using CH we construct examples of sequential topological groups: 1. a pair of countable Fréchet topological groups whose product is sequential but is not Fréchet, 2. a countable Fréchet and $α_1$ topological group which contains no copy of the rationals.
2
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Fixed point theory for multivalued maps in Fréchet spaces via degree and index theory

100%
Agarwal R., O'Regan D., Sahu D.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2007
|
tom 27
|
nr 2
399-409
EN
New fixed point results are presented for multivalued maps defined on subsets of a Fréchet space E. The proof relies on the notion of a pseudo open set, degree and index theory, and on viewing E as the projective limit of a sequence of Banach spaces.
3

Fixed point theory for multimaps defined on closed subsets of Fréchet spaces: the projective limit approach

100%
Agarwal R. P., O’Regan D.
Commentationes Mathematicae
|
2006
|
tom 46
|
nr 2
EN
New fixed point results are presented for maps defined on closed subsets of a Fréchet space \(E\). The proof relies on fixed point results in Banach spaces and viewing \(E\) as the projective limit of a sequence of Banach spaces.
4
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Functor of extension in Hilbert cube and Hilbert space

100%
Niemiec P.
Open Mathematics
|
2014
|
tom 12
|
nr 6
887-895
EN
It is shown that if Ω = Q or Ω = ℓ 2, then there exists a functor of extension of maps between Z-sets in Ω to mappings of Ω into itself. This functor transforms homeomorphisms into homeomorphisms, thus giving a functorial setting to a well-known theorem of Anderson [Anderson R.D., On topological infinite deficiency, Michigan Math. J., 1967, 14, 365–383]. It also preserves convergence of sequences of mappings, both pointwise and uniform on compact sets, and supremum distances as well as uniform continuity, Lipschitz property, nonexpansiveness of maps in appropriate metrics.
5
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Existence of mild solutions for semilinear differential equations with nonlocal and impulsive conditions

88%
Olszowy L.
Open Mathematics
|
2014
|
tom 12
|
nr 4
623-635
EN
This paper is concerned with the existence of mild solutions for impulsive semilinear differential equations with nonlocal conditions. Using the technique of measures of noncompactness in Banach and Fréchet spaces of piecewise continuous functions, existence results are obtained both on bounded and unbounded intervals, when the impulsive functions and the nonlocal item are not compact in the space of piecewise continuous functions but they are continuous and Lipschitzian with respect to some measure of noncompactness, and the linear part generates only a strongly continuous evolution system.
6
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The space of real-analytic functions has no basis

75%
Domański P., Vogt D.
Studia Mathematica
|
2000
|
tom 142
|
nr 2
187-200
EN
Let Ω be an open connected subset of $ℝ^d$. We show that the space A(Ω) of real-analytic functions on Ω has no (Schauder) basis. One of the crucial steps is to show that all metrizable complemented subspaces of A(Ω) are finite-dimensional.
7
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Existence and attractivity for fractional order integral equations in Fréchet spaces

75%
Abbas S., Benchohra M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2013
|
tom 33
|
nr 1
47-63
EN
In this paper, we present some results concerning the existence and the attractivity of solutions for some functional integral equations of Riemann-Liouville fractional order, by using an extension of the Burton-Kirk fixed point theorem in the case of a Fréchet space.
8
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An existence theorem for an hyperbolic differential inclusion in Banach spaces

75%
Benchohra M., Ntouyas S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2002
|
tom 22
|
nr 1
5-16
EN
In this paper, we investigate the existence of solutions on unbounded domain to a hyperbolic differential inclusion in Banach spaces. We shall rely on a fixed point theorem due to Ma which is an extension to multivalued between locally convex topological spaces of Schaefer's theorem.
9
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Factorization of Montel operators

75%
Dierolf S., Domański P.
Studia Mathematica
|
1993
|
tom 107
|
nr 1
15-32
EN
Consider the following conditions. (a) Every regular LB-space is complete; (b) if an operator T between complete LB-spaces maps bounded sets into relatively compact sets, then T factorizes through a Montel LB-space; (c) for every complete LB-space E the space C (βℕ, E) is bornological. We show that (a) ⇒ (b) ⇒ (c). Moreover, we show that if E is Montel, then (c) holds. An example of an LB-space E with a strictly increasing transfinite sequence of its Mackey derivatives is given.
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