Generic Uniqueness of Solutions for a Class of Vector Ky Fan Inequalities

Generic Uniqueness of Solutions for a Class of Vector Ky Fan Inequalities

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Article ID: iaor20126129
Volume: 155
Issue: 1
Start Page Number: 165
End Page Number: 179
Publication Date: Oct 2012
Journal: Journal of Optimization Theory and Applications
Authors: , ,
Keywords: vector optimization, Ky Fan inequality
Abstract:

This paper is intended mainly to present some generic uniqueness results for a class of vector Ky Fan inequalities. By employing the methods of set‐valued analysis, we prove that, in the sense of Baire category, most of the problems in a complete metric space, consisting of vector Ky Fan inequalities satisfying some conditions, have unique solution and that every vector Ky Fan inequality, possessing more than one solution, can be approached arbitrarily by a sequence of vector Ky Fan inequalities each of which has a unique solution. Our discussions are under two different settings. One setting is related to vector Ky Fan inequalities defined on a compact set; the other is related to vector Ky Fan inequalities defined on a noncompact set. The corollaries of our results generalized the corresponding results in the literature.

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