Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Zapraszamy na https://bibliotekanauki.pl
Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
Introduction
The main result of this paper is concerned with the conditions which guarantee that a multifunction $f: C → 2^X$ defined on an arbitrary subset C of a topological vector space X admits a point x of C such that x∈f(x).
First, we give some definitions and propositions which are associated with semicontinuous multifunctions (Part 1).
Next, in Part 2, we present a global convergence criterion on variable dimension algorithms for finding an approximate solution of the equation x∈f(x), and then we consider some fixed point theorems for multifunctions defined in finite-dimensional spaces.
Part 3 contains fixed point theorems for quasi upper semicontinuous multifunctions defined on arbitrary domains of topological vector spaces which generalize the theorems with boundary conditions.
Part 4 is devoted to some fixed point theorems for strongly lower semicontinuous multifunctions and thus here we are first concerned with fixed point theorems under boundary conditions for this class of multi-functions.
The last part shows how we can apply the results obtained to existence problem of equilibrium situations in the theory of non-cooperative games.
The main result of this paper is concerned with the conditions which guarantee that a multifunction $f: C → 2^X$ defined on an arbitrary subset C of a topological vector space X admits a point x of C such that x∈f(x).
First, we give some definitions and propositions which are associated with semicontinuous multifunctions (Part 1).
Next, in Part 2, we present a global convergence criterion on variable dimension algorithms for finding an approximate solution of the equation x∈f(x), and then we consider some fixed point theorems for multifunctions defined in finite-dimensional spaces.
Part 3 contains fixed point theorems for quasi upper semicontinuous multifunctions defined on arbitrary domains of topological vector spaces which generalize the theorems with boundary conditions.
Part 4 is devoted to some fixed point theorems for strongly lower semicontinuous multifunctions and thus here we are first concerned with fixed point theorems under boundary conditions for this class of multi-functions.
The last part shows how we can apply the results obtained to existence problem of equilibrium situations in the theory of non-cooperative games.
CONTENTS
Introduction..........................................................................................................5
1. Some classes of semicontinuous multifunctions...............................................5
2. A remark on the convergence of variable dimension algorithms.......................9
3. Some fixed point theorems.............................................................................15
4. Fixed point theorems for strongly lower semicontinuous multifunctions..........24
5. Some applications in game theory..................................................................29
References.........................................................................................................34
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
245
Liczba stron
35
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCXLV
Daty
wydano
1985
Twórcy
autor
- Institute of Computer Science, Polish Academy of Sciences, Poland
- Institute of Mathematics, Hanoi, S. R. Vietnam
Bibliografia
- [1] G. Allen, Variational inequalities, complementarity problems, and duality theorems, J. Math. Anal. App. 58, 1977, 1-10.
- [2] F. E. Browder, The fixed point theory of multivalued mappings in topological vector spaces, Math. Ann. 117, 1968, 283-301.
- [3] F. E. Browder, Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc. 74, 1968, 660-665.
- [4] Būi Cong Cuōng, Nash equilibrium point in n-persons games and in economics, Mathematics, Inst, of Math, Hanoi, 1976, 10-16 (in Vietnamese).
- [5] Būi Cong Cuōng, Some classes of games with multipayoffs, Scientific Bulletin Sci. Resear. Center of Vietnam, Hanoi, 1981, No. 2, 1-7 (in Vietnamese).
- [6] Būi Cong Cuōng, Some fixed point theorems for multifunctions in topological vector spaces (announcement of results), Bull. Pol. Acad. Sci., Math, (to appear).
- [7] J. Dungundji, A. Granas, Fixed point theory, Vol. I, Monografie Matematyczne, Polish Scientific Publishers, Warsaw 1982.
- [8] R. Engelking, General Topology, Monografie Matematyczne, Tom 60, Polish Scientific Publishers, Warsaw 1977.
- [9] Fan Ky, A generalizataion of Tychonoff's fixed point theorem, Math. Ann. 142, 1961, 305-310.
- [10] Fan Ky, Extensions of two fixed point theorems of F. E. Browder, Math. Z. 112, 1969, 234-230.
- [11] Fan Ky, A minimax inequality and applications, Inequalities III, O. Shioha, Ed., Academic Press, 1972, 103-113.
- [12] Fan Ky, Fixed point and related theorems for non-compact convex sets, Game Theory and Related Topics, O. Moeschlin, D. Pallaschke, Eds., North-Holland Publ. Comp., 1979, 151-156.
- [13] W. Forster, Ed., Numerical Solution of Highly Nonlinear Problems, North-Holland Pub. Comp., 1980.
- [14] B. Knaster, K. Kuratowski and S. Mazurkiewicz, Ein Beweis des Fispunktsatzes für n-dimensionale Simplexe, Fund. Math. 14, 1929, 132-137.
- [15] K. Kuratowski, Topologie I et II, Monografie Matematyczne, Polish Scientific Publishers, Warsaw 1958, 1961.
- [16] V. Laan, A. J. J. Talman, Convergence and properties of recent variable dimension algorithms, in [13], W. Forster, Ed., 1980, 3-36.
- [17] J. Leray, J. Schauder, Topologie et equations fonctionelles, Ann. Sci. Ecole Nor. Sup., Paris 51, 1934, 45-78,
- [18] B. Halpern, Fixed point theorems for set-valued mappings in infinite-dimensional space, Math. Ann. 189, 87-98.
- [19] Hoāng Tuy, Solving equation 0∈f(x) under general boundary conditions, in [13], W. Forster, Ed., 1980, 271-298.
- [20] Hoāng Tuy, On variable dimension algorithms and algorithms using primitive sets, Math. Operation. Statist., Ser. Optimization, 12, 3, 1981, 361-381.
- [21] L. S. Shapley, Equilibrium points in games with vector payoffs, Naval Res. Log. Quart. 6, 1, 57-62.
- [22] R. T. Rockaffeller, Convex analysis, Princeton, New York 1969.
- [23] N. Bourbaki, Espaces vectoriels topologiques, Chapitre 1 et 2 Deuxième edition, Hermann, Paris 1966.
- [24] G. Owen, Game Theory, Philadelphia, Saunders 1968.
Języki publikacji
| EN |
Uwagi
Identyfikator YADDA
bwmeta1.element.zamlynska-155138a6-b463-4568-8480-751bd0931946
Identyfikatory
ISBN
83-01-06471-4
ISSN
0012-3862
Kolekcja
DML-PL
Zawartość książki
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.