2017
Том 69
№ 9

All Issues

On properties of subdifferential mappings in Fréchet spaces

Kasyanov P. O., Mel'nik V. S.

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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.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 10, pp 1621-1634.

Citation Example: Kasyanov P. O., Mel'nik V. S. On properties of subdifferential mappings in Fréchet spaces // Ukr. Mat. Zh. - 2005. - 57, № 10. - pp. 1385–1394.

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