Metrically convex functions in normed spaces
Studia Mathematica (1993)
- Volume: 105, Issue: 1, page 1-11
- ISSN: 0039-3223
Access Full Article
top
Abstract
topHow to cite
topKryński, Stanisław. "Metrically convex functions in normed spaces." Studia Mathematica 105.1 (1993): 1-11. <http://eudml.org/doc/215980>.
@article{Kryński1993,
abstract = {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.},
author = {Kryński, Stanisław},
journal = {Studia Mathematica},
keywords = {metrically convex functions; normed spaces},
language = {eng},
number = {1},
pages = {1-11},
title = {Metrically convex functions in normed spaces},
url = {http://eudml.org/doc/215980},
volume = {105},
year = {1993},
}
TY - JOUR
AU - Kryński, Stanisław
TI - Metrically convex functions in normed spaces
JO - Studia Mathematica
PY - 1993
VL - 105
IS - 1
SP - 1
EP - 11
AB - 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.
LA - eng
KW - metrically convex functions; normed spaces
UR - http://eudml.org/doc/215980
ER -
References
top- [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. Zbl0336.46001
- [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). Zbl0811.52001
- [6] K. Menger, Untersuchungen über allgemeine Metrik, Math. Ann. 100 (1928), 75-163.
- [7] R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton 1970. Zbl0193.18401
- [8] V. P. Soltan, Introduction to the Axiomatic Theory of Convexity, Shtinitsa, Kishinev 1984 (in Russian). Zbl0559.52001
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.