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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Homological methods in fixed-point theory of multi-valued maps

100%
Górniewicz L.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS   Introduction................................................................. 5 I. HOMOLOGY   1. Preliminaries............................................................. 7   2. Maps in spaces of finite type............................................. 9   3. The Čech homology functor with compact carriers........................... 11   4. Vietoris maps............................................................. 13   5. Homology of open subsets of Euclidean spaces.............................. 14 II. THE LEFSCHETZ NUMBER   1. The (ordinary) Lefschetz number........................................... 18   2. The generalized Lefschetz number.......................................... 20 III. MULTI-VALUED MAPS   1. Upper semi-continuous and compact multi-valued mapB....................... 24   2. Admissible maps........................................................... 26   3. Homotopy and selectors.................................................... 9   4. Lefschetz maps............................................................ 30 IV. ANB-s, AANR-B and w-AANB-s   1. ANR-s..................................................................... 32   2. Approximation Theorem..................................................... 33   3. AANR-B.................................................................... 34   4. w-AANR-s.................................................................. 36 V. THE LEFSCHETZ FIXED-POINT THEOREM   1. The index of coincidence.................................................. 37   2. The Lefschetz Fixed-Point Theorem for open subsets in $R^n$............... 40   3. The Lefschetz Fixed-Point Theorem for AANR-s.............................. 41   4. Neighbourhood fixed-point property........................................ 45   5. The Lefschetz Fixed-Point Theorem for w-AANR-s............................ 46   6. Two consequences of the Lefschetz Fixed-Point Theorem..................... 47 VI. FIXED-POINT PROPERTY OP THE TYCHONOFF CUBE   1. Almost fixed points....................................................... 51   2. Fixed-point property for infinite products................................ 51
2
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On the Schauder fixed point theorem

60%
Górniewicz L., Rozpłoch-Nowakowska D.
Banach Center Publications
|
1996
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tom 35
|
nr 1
207-219
EN
The paper contains a survey of various results concerning the Schauder Fixed Point Theorem for metric spaces both in single-valued and multi-valued cases. A number of open problems is formulated.
3
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Once More on the Lefschetz Fixed Point Theorem

60%
Górniewicz L., Ślosarski M.
Bulletin of the Polish Academy of Sciences. Mathematics
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2007
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tom 55
|
nr 2
161-170
EN
An abstract version of the Lefschetz fixed point theorem is presented. Then several generalizations of the classical Lefschetz fixed point theorem are obtained.
4
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An Invariance Problem for Control Systems with Deterministic Uncertainty

60%
Górniewicz L., Nistri P.
Banach Center Publications
|
1996
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tom 35
|
nr 1
193-205
EN
This paper deals with a class of nonlinear control systems in $R^n$ in presence of deterministic uncertainty. The uncertainty is modelled by a multivalued map F with nonempty, closed, convex values. Given a nonempty closed set $K ⊂ R^n$ from a suitable class, which includes the convex sets, we solve the problem of finding a state feedback ū(t,x) in such a way that K is invariant under any system dynamics f. As a system dynamics we consider any continuous selection of the uncertain controlled dynamics F.
5
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Partially dissipative periodic processes

49%
Andres J., Górniewicz L., Lewicka M.
Banach Center Publications
|
1996
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tom 35
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nr 1
109-118
EN
Further extension of the Levinson transformation theory is performed for partially dissipative periodic processes via the fixed point index. Thus, for example, the periodic problem for differential inclusions can be treated by means of the multivalued Poincaré translation operator. In a certain case, the well-known Ważewski principle can also be generalized in this way, because no transversality is required on the boundary.
6
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Fractional order impulsive partial hyperbolic differential inclusions with variable times

49%
Abbas S., Benchohra M., Górniewicz L.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2011
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tom 31
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nr 1
91-114
EN
This paper deals with the existence of solutions to some classes of partial impulsive hyperbolic differential inclusions with variable times involving the Caputo fractional derivative. Our works will be considered by using the nonlinear alternative of Leray-Schauder type.
7
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Controllability on infinite time horizon for first and second order functional differential inclusions in Banach spaces

49%
Benchohra M., Górniewicz L., Ntouyas S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2001
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tom 21
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nr 2
261-282
EN
In this paper, we shall establish sufficient conditions for the controllability on semi-infinite intervals for first and second order functional differential inclusions in Banach spaces. We shall rely on a fixed point theorem due to Ma, which is an extension on locally convex topological spaces, of Schaefer's theorem. Moreover, by using the fixed point index arguments the implicit case is treated.
8
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The Lefschetz fixed point theorem for multivalued maps of non-metrizable spaces

48%
Fournier G., Górniewicz L.
Fundamenta Mathematicae
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1976
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tom 92
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nr 3
213-222
9
Content available remote

The Lefschetz fixed point theorem for some noncompact multi-valued maps

48%
Fournier G., Górniewicz L.
Fundamenta Mathematicae
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1977
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tom 94
|
nr 3
245-254
10
Content available remote

Fixed points of mapping in Klee admissible spaces

31%
Górniewicz L., Ślosarski M.
Control and Cybernetics
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2007
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tom 36
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nr 3
825-832
11
Content available remote

Preface, Contents

22%
Gęba K., Górniewicz L.
Banach Center Publications
|
1996
|
tom 35
|
nr 1
1-8
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