The fuzzy intersection rule in variational analysis with applications
type: Item
instance of: scholarly article
title: The fuzzy intersection rule in variational analysis with applications
zbMATH Open document ID: 1121.49019
author: Bingwu Wang
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-12-07T00:00:00Z
review text: The author discussed the fuzzy intersection rule for Frechet normal cones in Asplund spaces which was established by Mordukhovich and the author. In papers [(*) \textit{B. S.Mordukhovich} and \textit{B. Wang} [Nonlinear Anal. Theory Methods Appl. 47, No.~2, 717--728 (2001; Zbl 1042.49522); (**) J. Math. Anal. Appl. 272, No.~1, 164--186 (2002; Zbl 1006.49007)], only one form of the rule is obtained. A new form of the rule which seems to be more symmetric is derived in the present paper. It is shown that the new form is yet another characterization of the Asplund property, which is actually equivalent to the extremal principle. Some applications in addition to those in [(*), (**), \textit{B. S.Mordukhovich} and \textit{B. Wang}, J. Math. Anal. Appl. 282, No.~1, 63--84 (2003; Zbl 1033.49031)] are given. In particular, fuzzy calculus rules for Frechet constructions that includes an inverse image rule and functions/set-valued mappings under general settings are derived. These rules require no qualification condition, which may be more convenient in applications.
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 49J53
Mathematics Subject Classification ID: 46N10
zbMATH DE Number: 5077913
zbMATH Keywords: fuzzy intersection rule
zbMATH Keywords: fuzzy calculus
zbMATH Keywords: variational analysis
reviewed by: Xiao-Ping Yang
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.11.051
OpenAlex ID: W1963889989
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DOI: 10.1016/J.JMAA.2005.11.051
description: scientific article; zbMATH DE number 5077913