1Department of Mathematics Technion 32000 Haifa, Israel 2Department of Mathematics University of California, San Diego (UCSD) 9500 Gilman Drive La Jolla, CA 92093-0112, U.S.A.
Studia Mathematica, Tome 171 (2005) no. 2, pp. 125-152
We are given data $\alpha _1,\mathinner {\ldotp \ldotp \ldotp },\alpha _m$ and a set of points $E=\{ x_1,\mathinner {\ldotp \ldotp \ldotp },x_m\} $. We address the question of conditions ensuring the existence of a function $f$ satisfying the interpolation conditions $f(x_i)=\alpha _i$, $i=1,\mathinner {\ldotp \ldotp \ldotp },m$, that is also $n$-convex on a set properly containing $E$. We consider both one-point extensions of $E$, and extensions to all of ${{\mathbb R}}$. We also determine bounds on the $n$-convex functions satisfying the above interpolation conditions.
Keywords:
given alpha mathinner ldotp ldotp ldotp alpha set points mathinner ldotp ldotp ldotp address question conditions ensuring existence function satisfying interpolation conditions alpha mathinner ldotp ldotp ldotp n convex set properly containing consider one point extensions extensions mathbb determine bounds n convex functions satisfying above interpolation conditions
Affiliations des auteurs :
Allan Pinkus
1
;
Dan Wulbert
2
1
Department of Mathematics Technion 32000 Haifa, Israel
2
Department of Mathematics University of California, San Diego (UCSD) 9500 Gilman Drive La Jolla, CA 92093-0112, U.S.A.
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author = {Allan Pinkus and Dan Wulbert},
title = {Extending $n$-convex functions},
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Allan Pinkus; Dan Wulbert. Extending $n$-convex functions. Studia Mathematica, Tome 171 (2005) no. 2, pp. 125-152. doi: 10.4064/sm171-2-2
