Paraconvex functions and paraconvex sets

Huynh Van Ngai, and Jean-Paul Penot. "Paraconvex functions and paraconvex sets." Studia Mathematica 184.1 (2008): 1-29. <http://eudml.org/doc/284553>.

@article{HuynhVanNgai2008,
abstract = {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.},
author = {Huynh Van Ngai, Jean-Paul Penot},
journal = {Studia Mathematica},
keywords = {approximately convex function; approximately convex set; monotonicity; nonsmooth analysis; normal; projection; subdifferential},
language = {eng},
number = {1},
pages = {1-29},
title = {Paraconvex functions and paraconvex sets},
url = {http://eudml.org/doc/284553},
volume = {184},
year = {2008},
}

TY - JOUR
AU - Huynh Van Ngai
AU - Jean-Paul Penot
TI - Paraconvex functions and paraconvex sets
JO - Studia Mathematica
PY - 2008
VL - 184
IS - 1
SP - 1
EP - 29
AB - 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.
LA - eng
KW - approximately convex function; approximately convex set; monotonicity; nonsmooth analysis; normal; projection; subdifferential
UR - http://eudml.org/doc/284553
ER -