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    The best approximation theorems and variational inequalities for discontinuous mappings in Banach spaces

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    Fulltext not available
    Authors
    Liu, Lishan
    Kong, D.
    Wu, Yong Hong
    Date
    2015
    Type
    Journal Article
    
    Metadata
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    Citation
    Liu, L. and Kong, D. and Wu, Y.H. 2015. The best approximation theorems and variational inequalities for discontinuous mappings in Banach spaces. Science China Mathematics. 58 (12): pp. 2581-2592.
    Source Title
    Science China Mathematics
    DOI
    10.1007/s11425-015-5020-6
    ISSN
    1674-7283
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/42595
    Collection
    • Curtin Research Publications
    Abstract

    We discuss Ky Fan’s theorem and the variational inequality problem for discontinuous mappings f in a Banach space X. The main tools of analysis are the variational characterizations of the metric projection operator and the order-theoretic fixed point theory. Moreover, we derive some properties of the metric projection operator in Banach spaces. As applications of our best approximation theorems, three fixed point theorems for non-self maps are established and proved under some conditions. Our results are generalizations and improvements of various recent results obtained by many authors.

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