On a separation theorem for delta-convex functions

Andrzej Olbryś

Published: 2020-07-09

Vol. 34 No. 1 (2020)

On a separation theorem for delta-convex functions

Andrzej Olbryś

Abstract

In the present paper we establish necessary and sufficient conditions under which two functions can be separated by a delta-convex function. This separation will be understood as a separation with respect to the partial order generated by the Lorentz cone. An application to a stability problem for delta-convexity is also given.

Keywords:

convex functins , delta-convex function , Lorentz cone

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Olbryś, A. (2020). On a separation theorem for delta-convex functions. Annales Mathematicae Silesianae, 34(1), 133–141. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13638

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References

1. A.D. Aleksandrov, On surfaces represented as the difference of convex functions, Izvestiya Akad. Nauk Kazah. SSR. 60, Ser. Mat. Meh. 3, (1949), 3–20.
2. A.D. Aleksandrov, Surfaces represented by the differences of convex functions, Doklady Akad. Nauk SSSR (N.S.) 72, (1950), 613–616.
3. M.G. Arsove, Functions representable as differences of subharmonic functions, Trans. Amer. Math. Soc. 75 (1953), 327–365.
4. K. Baron, J. Matkowski, and K. Nikodem, A sandwich with convexity, Math. Pannon. 5 (1994), no. 1, 139–144.
5. H. Busemann and W. Feller, Krümmungseigenschaften Konvexer Flächen, Acta Math. 66 (1936), no. 1, 1–47.
6. P. Hartman, On functions representable as a difference of convex functions, Pacific J. Math. 9 (1959), 707–713.
7. C.O. Kiselman, Fonctions delta-convexes, delta-sousharmoniques et delta-plurisousharmoniques, in: P. Lelong (ed.), Séminaire Pierre Lelong (Analyse). Année 1975/76, Lecture Notes in Math., vol. 578, Springer-Verlag, Berlin, 1977, pp. 93–107.
8. A. Olbryś, On separation by h-convex functions, Tatra Mt. Math. Publ. 62 (2015), 105–111.
9. A. Olbryś, On sandwich theorem for delta-subadditive and delta-superadditive mappings, Results Math. 72 (2017), no. 1–2, 385–399.
10. A.W. Roberts and D.E. Varberg, Convex Functions, Pure and Applied Mathematics, vol. 57, Academic Press, New York-London, 1973.
11. L. Veselý and L. Zajiček, Delta-convex mappings between Banach spaces and applications, Dissertationes Math. (Rozprawy Mat.) 289 (1989), 52 pp. Google Scholar

Vol. 34 No. 1 (2020)
Published: 2020-07-20

ISSN: 0860-2107

eISSN: 2391-4238

10.2478/amsil

Publisher

University of Silesia Press

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