We study a class of functions which contains both convex functions and differentiable functions whose derivatives are locally Lipschitzian or Hölderian. This class is a subclass of the class of approximately convex functions. It enjoys refined properties. We also introduce a class of sets whose associated distance functions are of that type. We discuss the properties of the metric projections on such sets under some assumptions on the geometry of the Banach spaces in which they are embedded. We describe some relations between such sets and functions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm184-1-1,
author = {Huynh Van Ngai and Jean-Paul Penot},
title = {Paraconvex functions and paraconvex sets},
journal = {Studia Mathematica},
volume = {187},
year = {2008},
pages = {1-29},
zbl = {1181.49014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm184-1-1}
}
Huynh Van Ngai; Jean-Paul Penot. Paraconvex functions and paraconvex sets. Studia Mathematica, Tome 187 (2008) pp. 1-29. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm184-1-1/