TOPOLOGICAL METHODS IN THE FIXED-POINT THEORY OF MULTI-VALUED MAPS

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CONTENTS Introduction Chapter I. Approximative methods in the fixed-point theory of multi-valued maps § 1.1. Multi-valued maps and single-valued approximations § 1.2. The rotation of multi-valued vector fields with convex images and fixed-point theorems § 1.3. Obstruction theory and single-valued approximations of multi-valued maps § 1.4. Guide to the literature in Chapter I Chapter II. Homological methods in the fixed-point theory of multi-valued maps. The finite-dimensional case § 2.1. Formulation of a version of the Vietoris-Begle-Sklyarenko theorem § 2.2. The topological characteristic of a multi-valued vector field in a finite-dimensional space § 2.3. The rotation and the topological characteristic of -acyclic and generalized -acyclic multi-valued vector fields § 2.4. Some theorems on the computation of the topological characteristic § 2.5. Fixed-point theorems § 2.6. The Lefschetz theorem § 2.7. Guide to the literature in Chapter II Chapter III. Homological methods in the fixed-point theory of multi-valued maps. The infinite-dimensional case § 3.1. Partitions and the cohomology defined by them § 3.2. The topological characteristic of a multi-valued vector field in a Banach space § 3.3. The rotation of almost acyclic multi-valued vector fields § 3.4. Computation of the topological characteristic and fixed-point theorems § 3.5. Guide to the literature in Chapter III Appendix. Some applications References