Extending n-Convex Functions
نویسنده
چکیده
We are given data α1, . . . , αm and a set of points E = {x1, . . . , xm}. In this paper we address the question of conditions ensuring the existence of a function f satisfying the interpolation conditions f(xi) = αi, i = 1, . . . ,m, that is also n-convex on a set properly containing E. We consider both one point extensions of E, and extensions of E to all of IR. We also determine bounds on n-convex functions satisfying the above interpolation conditions. 2000 Mathematics Subject Classification. Primary 26A51, 41A05.
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تاریخ انتشار 2005