A divided difference inequality for n-convex functions |
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Authors: | D Zwick |
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Institution: | Department of Mathematics, University of Vermont, Burlington, Vermont 05405 U.S.A. |
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Abstract: | For a(1) ? a(2) ? ··· ? a(n) ? 0, b(1) ? b(2) ? ··· ? b(n) ? 0, the ordered values of ai, bi, i = 1, 2,…, n, m fixed, m ? n, and p ? 1 it is shown that where is the integer such that and . The inequality is shown to be sharp. When p < 1 and a(i)'s are in increasing order then the inequality is reversed. |
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Keywords: | |
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