# Metrically convex functions in normed spaces

Studia Mathematica (1993)

- Volume: 105, Issue: 1, page 1-11
- ISSN: 0039-3223

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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

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- [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