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

CONTENTSIntroduction 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

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