Topological Fixed Point Theory of Multivalued Mappings

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. G´orka, M. Go´rniewicz, S. Park and A. Wieczorek. The author wish to express his gratitude to P. Konstanty for preparing the electronic version of this monograph.