We investigate functions f: I → ℝ (where I is an open interval) such that for all u,v ∈ I with u < v and f(u) ≠ f(v) and each c ∈ (min(f(u),f(v)),max(f(u),f(v))) there is a point w ∈ (u,v) such that f(w) = c and f is approximately continuous at w.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm117-1-6,
author = {Zbigniew Grande},
title = {On a subclass of the family of Darboux functions},
journal = {Colloquium Mathematicae},
volume = {116},
year = {2009},
pages = {95-104},
zbl = {1177.26005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm117-1-6}
}
Zbigniew Grande. On a subclass of the family of Darboux functions. Colloquium Mathematicae, Tome 116 (2009) pp. 95-104. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm117-1-6/