The fuzzy intersection rule in variational analysis with applications
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.
scientific article; zbMATH DE number 5077913