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On properties of subdifferential mappings in Fréchet spaces

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Abstract

We present conditions under which the subdifferential of a proper convex lower-semicontinuous functional in a Fréchet space is a bounded upper-semicontinuous mapping. The theorem on the boundedness of a subdifferential is also new for Banach spaces. We prove a generalized Weierstrass theorem in Fréchet spaces and study a variational inequality with a set-valued mapping.

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Authors and Affiliations

  1. Shevchenko Kyiv National University, Kyiv

    P. O. Kas’yanov

  2. Institute of Applied System Analysis, Ukrainian Academy of Sciences, Ukrainian Ministry of Education and Science, Kyiv

    V. S. Mel’nyk

Authors
  1. P. O. Kas’yanov
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  2. V. S. Mel’nyk
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 10, pp. 1385–1394, October, 2005.

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Kas’yanov, P.O., Mel’nyk, V.S. On properties of subdifferential mappings in Fréchet spaces. Ukr Math J 57, 1621–1634 (2005). https://doi.org/10.1007/s11253-006-0017-5

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  • DOI: https://doi.org/10.1007/s11253-006-0017-5

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