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

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Title: Results on the fixed points of multifunctions with applications to problems in optimization and equilibrium theory
Author(s): Holly, Charles Anthony
Doctoral Committee Chair(s): McLinden, Lynn
Department / Program: Mathematics
Discipline: Mathematics
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): Mathematics Economics, Theory
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.
Issue Date: 1992
Type: Text
Language: English
URI: http://hdl.handle.net/2142/19147
Rights Information: Copyright 1992 Holly, Charles Anthony
Date Available in IDEALS: 2011-05-07
Identifier in Online Catalog: AAI9305553
OCLC Identifier: (UMI)AAI9305553
 

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