A NEW APPROACH TO THE DEFINITION ON TOPOLOGICAL DEGREE FOR MULTI-VALUED MAPPINGS.
Abstract
Multivalued mappings have become increasingly important in recent years in the mathematical theory of optimal control. In this paper, a certain approximation theorem on metric, locally convex spaces is used to obtain new simple proofs of fixed point theorems for multi-valued mappings. In particular, the antipodal theorem for multi-valued mappings is proved without the usual recourse to defining and using the concept of topological degree of a vector field. A new definition of topological degree is a consequence of this approach and some of the properties of this newly defined quantity are derived. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1969
- Accession Number
- AD0700110
Entities
People
- A Cellina
- A. Lasota
Organizations
- University of Maryland