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Extensions of generalized differential calculus in Asplund spaces

Bibliographic Details
Title: Extensions of generalized differential calculus in Asplund spaces
Authors: Bingwu Wang, Boris S. Mordukhovich
Source: Journal of Mathematical Analysis and Applications. 272:164-186
Publisher Information: Elsevier BV, 2002.
Publication Year: 2002
Subject Terms: Calculus of functions on infinite-dimensional spaces, generalized differential calculus, Asplund spaces, Applied Mathematics, Nonsmooth analysis, coderivatives, set-valued mappings, 0101 mathematics, subdifferentials, 01 natural sciences, normal cones, Analysis, Set-valued and variational analysis
Description: The authors give an extended generalized differential calculus for nonconvex normal cones to sets, coderivatives of set-valued mappings and subdifferentials of extended real-valued functions in infinite-dimensional vector spaces, especially in Asplund spaces. Based on different versions of the extremal principle, a fuzzy intersection rule for the Fréchet normal cone and especially an intersection rule for the limiting normal cones to sets in product spaces (with respect to different topologies on the duals) are established. As a consequence one gets a representation of the limiting normal cones to inverse images of set-valued mappings. In the second part, these results are used for the derivation of sum rules and chain rules for the limiting coderivatives of set-valued mappings and for the limiting subdifferentials of real-valued functions.
Document Type: Article
File Description: application/xml
Language: English
ISSN: 0022-247X
DOI: 10.1016/s0022-247x(02)00149-x
Access URL: https://www.sciencedirect.com/science/article/abs/pii/S0022247X0200149X
https://www.sciencedirect.com/science/article/pii/S0022247X0200149X
Rights: Elsevier Non-Commercial
Accession Number: edsair.doi.dedup.....6b0bd1af85856b8553fe7e10201c4e5d
Database: OpenAIRE
Description
ISSN:0022247X
DOI:10.1016/s0022-247x(02)00149-x