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    About Extensions of the Extremal Principle

    81405.pdf (260.3Kb)
    Access Status
    Open access
    Authors
    Bui, Hoa
    Kruger, A.Y.
    Date
    2018
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Bui, H.T. and Kruger, A.Y. 2018. About Extensions of the Extremal Principle. Vietnam Journal of Mathematics. 46 (2): pp. 215-242.
    Source Title
    Vietnam Journal of Mathematics
    DOI
    10.1007/s10013-018-0278-y
    ISSN
    2305-221X
    Faculty
    Faculty of Science and Engineering
    School
    School of Electrical Engineering, Computing and Mathematical Sciences (EECMS)
    Funding and Sponsorship
    http://purl.org/au-research/grants/arc/DP160100854
    Remarks

    This is a post-peer-review, pre-copyedit version of an article published in Vietnam Journal of Mathematics. The final authenticated version is available online at: http://doi.org/10.1007/s10013-018-0278-y

    URI
    http://hdl.handle.net/20.500.11937/81341
    Collection
    • Curtin Research Publications
    Abstract

    © 2018, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. In this paper, after recalling and discussing the conventional extremality, local extremality, stationarity and approximate stationarity properties of collections of sets, and the corresponding (extended) extremal principle, we focus on extensions of these properties and the corresponding dual conditions with the goal to refine the main arguments used in this type of results, clarify the relationships between different extensions, and expand the applicability of the generalized separation results. We introduce and study new more universal concepts of relative extremality and stationarity and formulate the relative extended extremal principle. Among other things, certain stability of the relative approximate stationarity is proved. Some links are established between the relative extremality and stationarity properties of collections of sets and (the absence of) certain regularity, lower semicontinuity, and Lipschitz-like properties of set-valued mappings.

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