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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree

Faculty of Technical Physics and Applied Mathematics, Gdańsk University of Technology, ul. Narutowicza 11/12, 80-233 Gdańsk, Poland
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Mathematics 2020, 8(8), 1262; https://doi.org/10.3390/math8081262
Received: 30 June 2020 / Revised: 26 July 2020 / Accepted: 28 July 2020 / Published: 1 August 2020
(This article belongs to the Special Issue Topological Methods in Nonlinear Analysis)
Consider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn 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. View Full-Text
Keywords: set-valued mapping; G-space; locally Lipschitz mapping; Clarkés generalized gradient; equivariant degree; graph approximation set-valued mapping; G-space; locally Lipschitz mapping; Clarkés generalized gradient; equivariant degree; graph approximation
MDPI and ACS Style

Dzedzej, Z.; Gzella, T. Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree. Mathematics 2020, 8, 1262.

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