On a Separation Theorem for Delta-Convex Functions

• Autorzy: Andrzej Olbryś
• Języki publikacji: EN

Abstrakty

EN

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. (original abstract)

Słowa kluczowe

EN

Mathematics; Mathematical functions; Physics; Special theory of relativity

PL

Matematyka; Funkcje matematyczne; Fizyka; Szczególna teoria względności

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2020
• Tom: 34 (1)
• Strony: 133--141

Twórcy

autor

Andrzej Olbryś

• University of Silesia in Katowice, Poland

Bibliografia

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• M.G. Arsove, Functions representable as differences of subharmonic functions, Trans. Amer. Math. Soc. 75 (1953), 327-365.
• K. Baron, J. Matkowski, and K. Nikodem, A sandwich with convexity, Math. Pannon. 5 (1994), no. 1, 139-144.
• H. Busemann and W. Feller, Krümmungseigenschaften Konvexer Flächen, Acta Math. 66 (1936), no. 1, 1-47.
• P. Hartman, On functions representable as a difference of convex functions, Pacific J. Math. 9 (1959), 707-713.
• 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.
• A. Olbryś, On separation by h-convex functions, Tatra Mt. Math. Publ. 62 (2015), 105-111.
• A. Olbryś, On sandwich theorem for delta-subadditive and delta-superadditive mappings, Results Math. 72 (2017), no. 1-2, 385-399.
• A.W. Roberts and D.E. Varberg, Convex Functions, Pure and Applied Mathematics, vol. 57, Academic Press, New York-London, 1973.
• L. Veselý and L. Zajiček, Delta-convex mappings between Banach spaces and applications, Dissertationes Math. (Rozprawy Mat.) 289 (1989), 52 pp.

Identyfikatory

DOI

10.2478/amsil-2020-0013