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Second-order viability result in Banach spaces

100%
Aitalioubrahim M., Sajid S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2010
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tom 30
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nr 1
5-21
EN
We show the existence result of viable solutions to the second-order differential inclusion ẍ(t) ∈ F(t,x(t),ẋ(t)), x(0) = x₀, ẋ(0) = y₀, x(t) ∈ K on [0,T], where K is a closed subset of a separable Banach space E and F(·,·,·) is a closed multifunction, integrably bounded, measurable with respect to the first argument and Lipschitz continuous with respect to the third argument.
2
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Selections that characterize topological completeness

100%
van Mill J., Pelant J., Pol R.
Fundamenta Mathematicae
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1996
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tom 149
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nr 2
127-141
EN
We show that the assertions of some fundamental selection theorems for lower-semicontinuous maps with completely metrizable range and metrizable domain actually characterize topological completeness of the target space. We also show that certain natural restrictions on the class of the domains change this situation. The results provide in particular answers to questions asked by Engelking, Heath and Michael [3] and Gutev, Nedev, Pelant and Valov [5].
3
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Trivial bundles of spaces of probability measures and countable-dimensionality

88%
Gutev V. G.
Studia Mathematica
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1995
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tom 114
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nr 1
1-11
EN
The probability measure functor P carries open continuous mappings $f: X onto → Y$ of compact metric spaces into Q-bundles provided Y is countable-dimensional and all fibers $f^{-1}(y)$ are infinite. This answers a question raised by V. Fedorchuk.
4
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Polynomial selections and separation by polynomials

63%
Wąsowicz S.
Studia Mathematica
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1996
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tom 120
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nr 1
75-82
EN
K. Nikodem and the present author proved in [3] a theorem concerning separation by affine functions. Our purpose is to generalize that result for polynomials. As a consequence we obtain two theorems on separation of an n-convex function from an n-concave function by a polynomial of degree at most n and a stability result of Hyers-Ulam type for polynomials.
5
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Hyperspace retractions for curves

53%
Charatonik J. J., Charatonik W. J., Omiljanowski K., Prajs J. R.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS 1. Introduction...................................5 2. Preliminaries.................................7 3. Hyperspace retractions.................9 4. Applications to selections............15 5. Applications to means.................18 References.....................................32
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