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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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