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Hahn–Banach theorems in nonstandard normed interval spaces

✍ Scribed by Hsien-Chung Wu

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
533 KB
Volume
72
Category
Article
ISSN
0362-546X

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✦ Synopsis

The conventional Hahn-Banach extension theorem based on vector space has been widely used to obtain many important and interesting results in nonlinear analysis, vector optimization and mathematical economics. Although the interval space is not a real vector space, the Hahn-Banach extension theorems based on interval spaces and nonstandard normed interval spaces can still be derived in this paper, which also shows the possible applications by considering the interval-valued problems in nonlinear analysis, vector optimization and mathematical economics.

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## Abstract We prove a nonstandard density result. It asserts that if a particular formula is true for functions in a set __K__ of linear continuous functions between Banach spaces __E__ and __D__, then it remains valid for functions that are limits, in the uniform convergence topology on a given c