A short proof of a theorem on compositions of d.c. mappings

Veselý, Libor

doi:10.1090/S0002-9939-1987-0911033-4

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A short proof of a theorem on compositions of d.c. mappings
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Proc. Amer. Math. Soc. 101 (1987), 685-686 Request permission

Abstract:

In this note, there is presented an essentially shorter proof of the theorem that a composition of d.c. mappings is locally d.c., proved for finite dimensions by P. Hartman in 1959.

References

Philip Hartman, On functions representable as a difference of convex functions, Pacific J. Math. 9 (1959), 707–713. MR 110773, DOI 10.2140/pjm.1959.9.707
A. Wayne Roberts and Dale E. Varberg, Convex functions, Pure and Applied Mathematics, Vol. 57, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1973. MR 0442824