We are given data α₁,..., αₘ and a set of points E = x₁,...,xₘ. We address the question of conditions ensuring the existence of a function f satisfying the interpolation conditions , i = 1,...,m, that is also n-convex on a set properly containing E. We consider both one-point extensions of E, and extensions to all of ℝ. We also determine bounds on the n-convex functions satisfying the above interpolation conditions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm171-2-2,
author = {Allan Pinkus and Dan Wulbert},
title = {Extending n-convex functions},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {125-152},
zbl = {1079.26004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm171-2-2}
}
Allan Pinkus; Dan Wulbert. Extending n-convex functions. Studia Mathematica, Tome 166 (2005) pp. 125-152. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm171-2-2/