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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Quadratic integral equations in reflexive Banach space

100%
Salem H.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2010
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tom 30
|
nr 1
61-69
EN
This paper is devoted to proving the existence of weak solutions to some quadratic integral equations of fractional type in a reflexive Banach space relative to the weak topology. A special case will be considered.
2
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Kneser's theorems for strong, weak and pseudo-solutions of ordinary differential equations in Banach spaces

100%
Cichoń M., Kubiaczyk I.
Annales Polonici Mathematici
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1995
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tom 62
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nr 1
13-21
EN
We investigate the structure of the set of solutions of the Cauchy problem x' = f(t,x), x(0) = x₀ in Banach spaces. If f satisfies a compactness condition expressed in terms of measures of weak noncompactness, and f is Pettis-integrable, then the set of pseudo-solutions of this problem is a continuum in $C_{w}(I,E)$, the space of all continuous functions from I to E endowed with the weak topology. Under some additional assumptions these solutions are, in fact, weak solutions or strong Carathéodory solutions, so we also obtain Kneser-type theorems for these classes of solutions.
3
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Retarded functional differential equations in Banach spaces and Henstock-Kurzweil-Pettis integrals

88%
Sikorska-Nowak A.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2007
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tom 27
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nr 2
315-327
EN
We prove an existence theorem for the equation x' = f(t,xₜ), x(Θ) = φ(Θ), where xₜ(Θ) = x(t+Θ), for -r ≤ Θ < 0, t ∈ Iₐ, Iₐ = [0,a], a ∈ R₊ in a Banach space, using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function f are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function f satisfies some conditions expressed in terms of the measure of weak noncompactness.
4
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Conical measures and properties of a vector measure determined by its range

88%
Rodríguez-Piazza L., Romero-Moreno M. C.
Studia Mathematica
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1997
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tom 125
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nr 3
255-270
EN
We characterize some properties of a vector measure in terms of its associated Kluvánek conical measure. These characterizations are used to prove that the range of a vector measure determines these properties. So we give new proofs of the fact that the range determines the total variation, the σ-finiteness of the variation and the Bochner derivability, and we show that it also determines the (p,q)-summing and p-nuclear norm of the integration operator. Finally, we show that Pettis derivability is not determined by the range and study when every measure having the same range of a given measure has a Pettis derivative.
5
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Translations of functions iv vector Hardy classes on the unit disk

65%
Michalak A.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS    Introduction...................................................................................................5 0. Preliminaries................................................................................................7 1. Fundamental properties of harmonic vector functions...............................13 2. Hardy spaces of vector functions...............................................................15    Relations between scalar and vector Hardy classes...................................15    The factorization theorem for $H^p(𝔻,X)$...................................................19    Nontangential limits of functions in $h^p(𝔻,X)$...........................................22    Properties of functions in $h^p(𝕋,X)$..........................................................27 3. Spaces $h^p(𝔻,X)$ and $M_p(𝕋,X)$..........................................................29 4. The sets of translates of harmonic functions..............................................33 5. Translations of functions from Hardy classes..............................................37 6. Translations of functions from Smirnov classes...........................................41 7. Translations of measures from $M_p(G,X)$................................................43 8. A criterion of uncomplementability of $L^p(λ_G,X)$ in $M_p(G,X)$.............53 9. Pettis integrability of the translation function for vector measures...............64    References...................................................................................................77
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