Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree

Zdzisław Dzedzej and Tomasz Gzella
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Zdzisław Dzedzej: Faculty of Technical Physics and Applied Mathematics, Gdańsk University of Technology, ul. Narutowicza 11/12, 80-233 Gdańsk, Poland
Tomasz Gzella: Faculty of Technical Physics and Applied Mathematics, Gdańsk University of Technology, ul. Narutowicza 11/12, 80-233 Gdańsk, Poland

Mathematics, 2020, vol. 8, issue 8, 1-14

Abstract: Consider the Euclidean space R n with the orthogonal action of a compact Lie group G . We prove that a locally Lipschitz G -invariant mapping f from R n to R can be uniformly approximated by G -invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarkés generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient mappings.

Keywords: set-valued mapping; G-space; locally Lipschitz mapping; Clarkés generalized gradient; equivariant degree; graph approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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