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.
@article{bwmeta1.element.bwnjournal-article-smv105i1p1bwm,
author = {Stanis\l aw Kry\'nski},
title = {Metrically convex functions in normed spaces},
journal = {Studia Mathematica},
volume = {104},
year = {1993},
pages = {1-11},
zbl = {0811.52001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv105i1p1bwm}
}
Kryński, Stanisław. Metrically convex functions in normed spaces. Studia Mathematica, Tome 104 (1993) pp. 1-11. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv105i1p1bwm/
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