Metrically convex functions in normed spaces

• Autorzy: Stanisław Kryński
• Języki publikacji: EN

Abstrakty

EN

Properties of metrically convex functions in normed spaces (of any dimension) are considered. The main result, Theorem 4.2, gives necessary and sufficient conditions for a function to be metrically convex, expressed in terms of the classical convexity theory.

Kategorie tematyczne

• 46B99: None of the above, but in this section
• 52A01: Axiomatic and generalized convexity
• 26A51: Convexity, generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1993
• Tom: 105
• Numer: 1
• Strony: 1-11

Daty

wydano

1993

otrzymano

1989-09-29

poprawiono

1992-09-30

Twórcy

autor

Stanisław Kryński

• Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warszawa, Poland

Bibliografia

• [1] T. T. Arkhipova and I. V. Sergenko, The formalization and solution of certain problems of organizing the computing process in data processing systems, Kibernetika 1973 (5), 11-18 (in Russian).
• [2] L. M. Blumenthal, Theory and Applications of Distance Geometry, Oxford University Press, Oxford 1953.
• [3] V. G. Boltyanskiĭ and P. S. Soltan, Combinatorial Geometry of Various Classes of Convex Sets, Shtinitsa, Kishinev 1978 (in Russian).
• [4] R. B. Holmes, Geometric Functional Analysis and Its Applications, Springer, New York 1975.
• [5] S. L. Kryński, Characterization of metrically convex functions in normed spaces, Ph.D. thesis, Institute of Mathematics, Polish Academy of Sciences, Warszawa 1988 (in Polish).
• [6] K. Menger, Untersuchungen über allgemeine Metrik, Math. Ann. 100 (1928), 75-163.
• [7] R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton 1970.
• [8] V. P. Soltan, Introduction to the Axiomatic Theory of Convexity, Shtinitsa, Kishinev 1984 (in Russian).