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Tytuł książki

Fixed point index theory for a class of nonacyclic multivalued maps

Autorzy

Zdzisław Dzedzej

Seria

Rozprawy Matematyczne tom/nr w serii: 253 wydano: 1985

Zawartość

Pełne teksty:
rm25301.pdf

Warianty tytułu

Abstrakty

EN

CONTENTS
0. Introduction.....................................................................5
I. Homology.........................................................................6
II. Multivalued maps...........................................................11
III. Chain approximations and index...................................15
IV. Chain approximations of decompositions of maps........18
V. Index of decompositions for compact polyhedra............26
VI. Index of decompositions for compact ANR's.................31
VII. Index of decompositions for arbitrary ANR's................38
VIII. Applications of the index to multivalued maps............42
IX. The Nielsen theory.......................................................47
References.......................................................................52

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 253

Liczba stron

53

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CCLIII

Daty

wydano
1985

Twórcy

autor
Zdzisław Dzedzej

Bibliografia

  • [1] E. G. Begle, The Vietoris mapping theorem for bicompact spaces, Ann. of Math. 51 (1950), 534-543.
  • [2] C. Berge, Espaces Topologiques. Fonctions Multivoques, Dunod, Paris 1959.
  • [3] H. F. Bohnenblust and S. Karlin, On a theorem of Ville, in: Contributions to the Theory of Games. Vol. I, Ann. of Math. Stud, Princeton 1950.
  • [4] Yu. G. Borisovich, B. D. Gel'man, A. D. Myshkis and V. V. Obukhovskii, Topological methods in the theory of fixed points of multivalued mappings (in Russian), Uspiekhi Mat. Nauk 35 (1) (1980), 59-126.
  • [5] C. Bowszyc, Fixed points theorems for the pairs of spaces, Bull. Acad. Polon. Sci. 16 (1968), 845-851.
  • [6] R. F. Brown, The Lefschetz Fixed Point Theorem, Scott, Foresman and Co., Glenview, 111., London 1971.
  • [7] B. D. Calvert, The local fixed point index for multivalued transformations in a Banach space, Math. Ann. 190 (1970), 119-128.
  • [8] A. Dold, Fixed point index and fixed point theorems for Euclidean neighbourhood retracts, Topology 4 (1965), 1-8.
  • [9] J. Dugundji and A. Granas, Fixed Point Theory, I, Monograf. Mat. 61, PWN, Warszawa 1982.
  • [10] S. Eilenberg and D. Montgomery, Fixed point theorems for multivalued transformations, Amer. J. Math. 58 (1946), 214-222.
  • [11] S. Eilenberg and N. Steenrod, Foundations of Algebraic Topology, Princeton Univ. Press, Princeton 1952.
  • [12] Ky Fan, Fixed point and minimax theorems in locally convex topological linear spaces, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 271-275.
  • [13] C. C. Fenske and H. O. Peitgen, Attractors and the fixed point index for a class of multivalued mappings. Bull. Acad. Polon. Sci. 25 (1977), 477-487.
  • [14] G. Fournier, A simplicial approach to the fixed point index, in: Lecture Notes in Math. 886, 1981, 73-102.
  • [15] G. Fournier and L. Gorniewicz, The Lefschetz fixed point theorem for some non-compact multivalued maps, Fund. Math. 94 (1977), 245-254.
  • [16] J. Girolo, Approximating compact sets in normed linear spaces. Pacific J. Math. 98 (1982), 81-89.
  • [17] L. Gorniewicz, A review of various results and problems of the fixed point theory of multivalued mappings, Preprint no. 1, Gdansk University, 1978.
  • [18] L. Gorniewicz, Homological methods in fixed point theory of multivalued maps, Dissertationes Math. 129 (1976), 71 pp.
  • [19] L. Gorniewicz, On the Lefschetz coincidence theorem, in: Lecture Notes in Math. 886, 1981, 116-139.
  • [20] L. Gorniewicz and H.O. Peitgen, Degeneracy, non-ejective fixed points and the fixed point index, J. Math. Pures Appl. 58(1979), 217-228.
  • [21] A. Granas, The Leray-Schauder index and the fixed point theory for arbitrary ANR's, Bull. Soc. Math. France 100 (1972), 209-228.
  • [22] P. J. Hilt on and S. Wylie, Homology Theory, Cambridge Univ. Press, 1960.
  • [23] J. Jezierski, The Nielsen relation for multivalued maps, to appear.
  • [24] Boju Jiang, Lectures on Nielsen Fixed Point Theory, AMS Publ., Contemporary Math. Ser. 14, Providence 1983.
  • [25] Z. Kucharski, A coincidence index, Bull. Acad. Polon. Sci. 24(1976), 245 252.
  • [26] Z. Kucharski, Two consequences of the coincidence index, Bull. Acad. Polon. Sci. 24 (1976), 437-444.
  • [27] A. Lasota and Z. Opial, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations. Bull. Acad. Polon. Sci. 13(1965), 781 786.
  • [28] A. Lasota and Z. Opial, Fixed point theorem for multivalued mappings and optimal control problems. Bull. Acad. Polon. Sci. 16 (1968), 645-649.
  • [29] S. Lefschetz, Algebraic Topology, AMS, Providence, R. I, New York 1942.
  • [30] B. O'Neill, Essential sets and fixed points, Amer. J. Math. 75 (1953), 497-509.
  • [31] B. O'Neill, Induced homology homomorphisms for set-valued maps, Pacific J. Math. 7 (1957), 1179-1184.
  • [32] S. N. Patnaik, Fixed points of multiple-valued transformations, Fund. Math. 65 (1969), 345-349.
  • [33] H. O. Peitgen, On the Lefschetz number for iterates of continuous mappings, Proc. Amer. Math. Soc. 54, (1976), 441-444.
  • [34] U. K. Scholz, The Nielsen fixed point theory for noncompact spaces. Rocky Mountain J. Math. 4 (1974), 81-87.
  • [35] H. Schirmer, An index and a Nielsen number for n-valued multifunctions, to appear.
  • [36] H. Schirmer, Fixed points, antipodal points and coincidences of n-acyclic valued multifunctions, in: Proc. Special Session on Fixed Points, AMS, Toronto 1982.
  • [37] W. Segiet, Local coincidence index for morphisms, Bull. Acad. Polon. Sci. 30 (1982), 261 267.
  • [38] H. W. Siegberg and G. Skordev, Fixed point index and chain approximations, Pacific J. Math. 102 (1982), 455-486.
  • [39] G. Skordev, Dissertation (in Bulgarian), University of Sofia, 1982.
  • [40] E. H. Spanier, Algebraic Topology, McGraw-Hill, New York 1966.
  • [41] L. Vietoris. Über den höheren Zusammenhang kompakter Räume und eine Klasse von zusammenhangstreuen Abbildungen, Math. Ann. 97 (1927), 454-472.
  • [42] S. A. Williams, An index for set-valued maps in infinite dimensional spaces, Proc. Amer. Math. Soc. 31 (1972), 557-563.

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bwmeta1.element.zamlynska-80353052-c9a3-4349-9585-b02a3ba90140

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ISBN
83-01-06648-2
ISSN
0012-3862

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DML-PL
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