University of Illinois Urbana-Champaign

Results on the fixed points of multifunctions with applications to problems in optimization and equilibrium theory

Holly, Charles Anthony

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https://hdl.handle.net/2142/19147

Description

Title
Results on the fixed points of multifunctions with applications to problems in optimization and equilibrium theory
Author(s)
Holly, Charles Anthony
Issue Date
1992
Doctoral Committee Chair(s)
McLinden, Lynn
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • Mathematics
  • Economics, Theory
Language
eng
Abstract
"In this thesis the techniques of multifunction theory are applied to problems in optimization and equilibrium theory. First, fixed point index theory for multifunctions is used to extend a continuation result of F. E. Browder. This extension is then used to obtain existence results for several types of variational inequality problems. In particular, extensions of Eaves' ""basic theorem of complementarity"" are given. Next, some outstanding questions are settled regarding the $\alpha$-core of an exchange economy. It is shown that an exchange economy with three or more agents can have an empty $\alpha$-core. Comparison is made with a well-known theorem of Scarf. Conditions under which an exchange economy (or an abstract economy) is guaranteed to have a nonempty $\alpha$-core are also presented. These latter results extend recent work of Florenzano and of Yannelis."
Type of Resource
text
Permalink
http://hdl.handle.net/2142/19147
Copyright and License Information
Copyright 1992 Holly, Charles Anthony

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