Characterization of convex functions
Studia Mathematica (2009)
- Volume: 192, Issue: 1, page 29-37
- ISSN: 0039-3223
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topJacek Tabor, and Józef Tabor. "Characterization of convex functions." Studia Mathematica 192.1 (2009): 29-37. <http://eudml.org/doc/285040>.
@article{JacekTabor2009,
abstract = {There are many inequalities which in the class of continuous functions are equivalent to convexity (for example the Jensen inequality and the Hermite-Hadamard inequalities). We show that this is not a coincidence: every nontrivial linear inequality which is valid for all convex functions is valid only for convex functions.},
author = {Jacek Tabor, Józef Tabor},
journal = {Studia Mathematica},
keywords = {convex function; Jensen inequality; Hermite-Hadamard inequality; approximation},
language = {eng},
number = {1},
pages = {29-37},
title = {Characterization of convex functions},
url = {http://eudml.org/doc/285040},
volume = {192},
year = {2009},
}
TY - JOUR
AU - Jacek Tabor
AU - Józef Tabor
TI - Characterization of convex functions
JO - Studia Mathematica
PY - 2009
VL - 192
IS - 1
SP - 29
EP - 37
AB - There are many inequalities which in the class of continuous functions are equivalent to convexity (for example the Jensen inequality and the Hermite-Hadamard inequalities). We show that this is not a coincidence: every nontrivial linear inequality which is valid for all convex functions is valid only for convex functions.
LA - eng
KW - convex function; Jensen inequality; Hermite-Hadamard inequality; approximation
UR - http://eudml.org/doc/285040
ER -
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