New results in the theory of multivalued mappings. I. Topological characteristics and solvability of operator relations

The first part of the survey describes the fundamental results in the theory of multivalued mappings, obtained during the period 1981–1986. The survey contains a description of fixed-point and coincidence theorems for various classes of multivalued mappings, generalizing a series of classical results. Results on the theory of the topological degree of multivalued mappings are also given.