Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
1-11
Opis fizyczny
Daty
wydano
1993
otrzymano
1989-09-29
poprawiono
1992-09-30
Twórcy
autor
- 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).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv105i1p1bwm