
Accession Number : AD0700110
Title : A NEW APPROACH TO THE DEFINITION ON TOPOLOGICAL DEGREE FOR MULTIVALUED 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 multivalued mappings. In particular, the antipodal theorem for multivalued 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