Level sets of continuous functions increasing with respect to each variable

Katarzyna Sajbura. "Level sets of continuous functions increasing with respect to each variable." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 25.1 (2005): 19-26. <http://eudml.org/doc/271441>.

@article{KatarzynaSajbura2005,
abstract = { We are going to prove that level sets of continuous functions increasing with respect to each variable are arcwise connected (Theorem 3) and characterize those of them which are arcs (Theorem 2). In [3], we will apply the second result to the classical linear functional equation φ∘f = gφ + h (cf., for instance, [1] and [2]) in a case not studied yet, where f is given as a pair of means, that is so-called mean-type mapping. },
author = {Katarzyna Sajbura},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {level set; continuous function; function increasing with respect to each variable; arcwise connectedness; arcwise connected level sets},
language = {eng},
number = {1},
pages = {19-26},
title = {Level sets of continuous functions increasing with respect to each variable},
url = {http://eudml.org/doc/271441},
volume = {25},
year = {2005},
}

TY - JOUR
AU - Katarzyna Sajbura
TI - Level sets of continuous functions increasing with respect to each variable
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2005
VL - 25
IS - 1
SP - 19
EP - 26
AB - We are going to prove that level sets of continuous functions increasing with respect to each variable are arcwise connected (Theorem 3) and characterize those of them which are arcs (Theorem 2). In [3], we will apply the second result to the classical linear functional equation φ∘f = gφ + h (cf., for instance, [1] and [2]) in a case not studied yet, where f is given as a pair of means, that is so-called mean-type mapping.
LA - eng
KW - level set; continuous function; function increasing with respect to each variable; arcwise connectedness; arcwise connected level sets
UR - http://eudml.org/doc/271441
ER -