Accession Number : AD0700110

Title :   A NEW APPROACH TO THE DEFINITION ON TOPOLOGICAL DEGREE FOR MULTI-VALUED MAPPINGS.

Descriptive Note : Technical note,

Corporate Author : MARYLAND UNIV COLLEGE PARK DEPT OF ELECTRICAL ENGINEERING

Personal Author(s) : Cellina,A ; Lasota,A.

Report Date : SEP 1969

Pagination or Media Count : 14

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)

Descriptors :   (*CONTROL SYSTEMS, MATHEMATICAL MODELS), (*MAPPING(TRANSFORMATIONS), TOPOLOGY), CONVEX SETS, APPROXIMATION(MATHEMATICS), THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE