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1
Content available 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
Content available remote Once More on the Lefschetz Fixed Point Theorem
58%
Górniewicz L. , Ślosarski M.
Bulletin of the Polish Academy of Sciences. Mathematics
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2007
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tom 55
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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.
3
Content available remote On the Schauder fixed point theorem
58%
Górniewicz L. , Rozpłoch-Nowakowska D.
Banach Center Publications
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1996
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tom 35
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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.
4
Content available remote An Invariance Problem for Control Systems with Deterministic Uncertainty
58%
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
Content available remote Partially dissipative periodic processes
47%
Andres J. , Górniewicz L. , Lewicka M.
Banach Center Publications
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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
Content available Controllability on infinite time horizon for first and second order functional differential inclusions in Banach spaces
47%
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.
7
Content available Fractional order impulsive partial hyperbolic differential inclusions with variable times
47%
Abbas S. , Benchohra M. , Górniewicz L.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2011
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tom 31
|
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.
8
Content available remote The Lefschetz fixed point theorem for multivalued maps of non-metrizable spaces
47%
Fournier G. , Górniewicz L.
Fundamenta Mathematicae
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1976
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tom 92
|
nr 3
213-222
9
Content available remote The Lefschetz fixed point theorem for some noncompact multi-valued maps
47%
Fournier G. , Górniewicz L.
Fundamenta Mathematicae
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1977
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tom 94
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nr 3
245-254
10
Content available remote Fixed points of mapping in Klee admissible spaces
30%
Górniewicz L. , Ślosarski M.
Control and Cybernetics
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2007
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tom 36
|
nr 3
825-832
11
Content available remote Preface, Contents
21%
Gęba K. , Górniewicz L.
Banach Center Publications
|
1996
|
tom 35
|
nr 1
1-8
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