Skiba R. Fixed points of multivalued weighted maps. - Toruń: Juliusz Schauder Center for nonlinear studies; Nicolaus Copernicus University, 2007. - 148 p. - (Lecture notes in nonlinear analysis; Vol. 9). - ISBN 978-83-231-2100-8  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

Preface ......................................................... 5 Chapter 1. Topological Backround ................................ 7 1.1. Preliminaries ........................................ 7 1.2. ARs and ANRs ......................................... 8 1.3. Multivalued mappings — general properties ........... 10 1.4. Direct and inverse limits ........................... 11 1.5. The Čech homology functor ........................... 12 1.6. The Lefschetz number ................................ 12 Chapter 2. ω-Maps .............................................. 17 2.1. Definitions and examples ............................ 17 2.2. Elementary properties ............................... 19 2.3. Darbo homology functor .............................. 26 2.3.1. Basic constructions .......................... 26 2.3.2. The homology cross products .................. 29 2.4. The ω-homotopy functor .............................. 32 2.5. The Lefschetz fixed point theory for ω-maps ......... 33 2.6. Topological degree for ω-maps ....................... 35 2.6.1. Topological degree in Rn ..................... 35 2.6.2. Topological degree in normed spaces .......... 45 2.7. Topological essentiality ............................ 52 2.8. Extension theorems .................................. 56 Chapter 3. Weighted Carriers ................................... 67 3.1. Definition and examples ............................. 67 3.2. Basic properties .................................... 71 Chapter 4. Approximation Methods ............................... 81 4.1. Graph-approximations ................................ 81 4.2. ω-UV-sets ........................................... 88 4.3. Existence of approximations ......................... 95 4.4. Bijection theorem .................................. 108 4.4.1. Induced homomorphisms ....................... 113 4.5. Fixed point theorems for ω-carriers ................ 118 4.6. Topological degree for compositions of ω-carriers ......................................... 128 Chapter 5. Remarks on the Nielsen Fixed Point Theory for Weighted Maps ...................................... 141 Bibliography .................................................. 145