Topological Fixed Point Theory of Multivalued Mappings - Topological Fixed Point Theory and Its Applications 2nd ed. 2006 edition

Marc Notes: Originally published as volume 495 in the series Mathematics and its Applications; Includes bibliographical references and index.; Based on pre-pub. info. only. Due date: July 2006. Table of Contents: Preface -- Preface to the second edition -- Chapter I. Background in Topology -- 1. Extension and embedding properties -- 2. Homotopical properties of spaces -- 3. Approximative and proximative retracts -- 4. Hyperspaces of metric spaces -- 5. The Cech homology (cohomology) functor -- 6. Maps of spaces of finite type -- 7. The Cech homology functor with compact carriers -- 8. Vietoris maps -- 9. Homology of open subsets of Euclidean spaces -- 10. The (ordinary) Lefschetz number -- 11. The generalized Lefschetz number -- 12. The coincidence problem -- Chapter II. Multivalued Mappings -- 13. General properties -- 14. Upper semicontinuous mappings -- 15. Lower semicontinuous mappings -- 16. Michael's selection theorem -- 17. ?-Selectionable mappings -- 18. Directionally continuous selections -- 19. Measurable selections -- 20. Borsuk and Hausdorff continuity of multivalued mappings -- 21. Banach contraction principle for multivalued maps -- Chapter III. Approximation Methods in Fixed Point Theory of Multivalued Mappings -- 22. Graph-approximation -- 23. Existence of approximations -- 24. Homotopy -- 25. The fixed point index in A(X) -- 26. Topological degree in Rn -- 27. Topological degree for mappings with non-compact values in Rn -- 28. Topological degree in normed spaces -- 29. Topological degree of vector fields with non-compact values in Banach spaces -- 30. Topological essentiality -- 31. Random fixed points -- Chapter IV. Homological Methods in Fixed Point Theory of Multivalued Mappings -- 32. Acyclic mappings -- 33. Strongly acyclic maps -- 34. The fixed point index for acyclic maps of Euclidean neighbourhood retracts -- 35. The Nielsen number -- 36. n-Acyclic mappings -- 37. Theorem on antipodes for n-acyclic mappings -- 38. Theorem on invariance of domain -- 39. n-Acyclic compact vector fields in normed spaces -- 40. Admissible mappings -- 41. The Lefschetz fixed point theorem for admissible mappings -- 42. The Lefschetz fixed point theorem for non-compact admissible mappings -- 43. n-Admissible mappings -- 44. Category of morphisms -- 45. The Lefschetz fixed point theorem for morphisms -- 46. Homotopical classification theorems for morphisms -- 47. The fixed point index for morphisms -- 48. Noncompact morphisms -- 49. n-Morphisms -- 50. Multivalued maps with nonconnected values -- 51. A fixed point index of decompositions for finite polyhedra -- 52. Fixed point index of decompositions for compact ANRs -- 53. Fixed point index of decompositions for arbitrary ANRs -- 54. Spheric mappings -- Chapter V. Consequences and Applications -- 55. Birkhoff-Kellog, Rothe and Poincare theorems -- 56. Fixed point property and families of multivalued mappings -- 57. The Lefschetz fixed point theorem for pairs of spaces -- 58. Repulsive and ejective fixed points -- 59. Condensing and k-set contraction mappings -- 60. Compacting mappings -- 61. Fixed points of differentiable multivalued maps -- 62. The generalized topological degree for acyclic mappings -- 63. The bifurcation index -- 64. Multivalued dynamical systems -- 65. Minimax theorems for ANRs -- 66. KKM-mappings -- 67. Topological dimension of the set of fixed points -- 68. On the basis problem in normed spaces -- Chapter VI. Fixed point theory approach to Differential Inclusions -- 69. Aronszajn type of results -- 70. Solution sets for differential inclusions -- 71. The lower semicontinuous case -- 72. Periodic solutions for differential inclusions in Rn -- 73. Differential inclusions on proximate retracts -- 74. Implicit differential inclusions -- 75. Concluding remarks and comments -- Chapter VII. Recent Results -- 76. Periodic invariants; the Euler-Poincare characteristic -- 77. The coincidence Nielsen number -- 78. Fixed points of symmetric product mappings -- 79. The category of weighted maps -- 80. Darbo homology functor and its applications to fixed point problems -- 81. More about spheric mappings -- 82. A coincidence index involving Fredholm operators -- 83. Fixed points of monotone-type multivalued operators -- 84. Multivalued Poincare operators -- 85. Multivalued fractals -- Bibliography -- Index. Publisher Marketing: This book is an attempt to give a systematic presentation of results and me- ods which concern the ?xed point theory of multivalued mappings and some of its applications. In selecting the material we have restricted ourselves to stu- ing topological methods in the ?xed point theory of multivalued mappings and applications, mainly to di?erential inclusions. Thus in Chapter III the approximation (on the graph) method in ?xed point theory of multivalued mappings is presented. Chapter IV is devoted to the ho- logical methods and contains more general results, e.g. the Lefschetz Fixed Point Theorem, the ?xed point index and the topological degree theory. In Chapter V applications to some special problems in ?xed point theory are formulated. Then in the last chapter a direct applications to di?erential inclusions are presented. Note that Chapters I and II have an auxiliary character, and only results c- nected with the Banach Contraction Principle (see Chapter II) are strictly related to topological methods in the ?xed point theory. In the last section of our book (see Section 75) we give a bibliographicalguide and also signalsome further results which are not contained in our monograph. The author thanks several colleagues and my wife Maria who read and c- mented on the manuscript. These include J. Andres, A. Buraczewski, G. Gabor, A. Gorka, M. Gorniewicz, S. Park and A. Wieczorek. The author wish to express his gratitude to P. Konstanty for preparing the electronic version of this monograph."