Ekeland's variational principle in Fréchet spaces and the density of extremal points

Volume 168 / 2005

J. H. Qiu Studia Mathematica 168 (2005), 81-94 MSC: 49J45, 46A04. DOI: 10.4064/sm168-1-6


By modifying the method of Phelps, we obtain a new version of Ekeland's variational principle in the framework of Fréchet spaces, which admits a very general form of perturbations. Moreover we give a density result concerning extremal points of lower semicontinuous functions on Fréchet spaces. Even in the framework of Banach spaces, our result is a proper improvement of the related known result. From this, we derive a new version of Caristi's fixed point theorem and a density result for Caristi fixed points.


  • J. H. QiuDepartment of Mathematics
    Suzhou University
    Suzhou, Jiangsu 215006
    People's Republic of China

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