Journal of Inequalities and Applications
Volume 1 (1997), Issue 4, Pages 301-310
doi:10.1155/S1025583497000209
Discrete inequalities of Wirtinger’s type for higher differences
Faculty of Electronic Engineering, Department of Mathematics, P.O. Box 73, Niš 18001, Serbia
Received 28 July 1996
Copyright © 1997 Gradimir V. Milovanović and Igor Ž. Milovanović. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Discrete version of Wirtinger’s type inequality for higher differences,
An,m∑k=1nxk2≤∑k=lmum(Δmxk)2≤Bn,m∑k=1nxk2,
where lm=1−[m/2],um=n−[m/2] and
Δmxk=∑i=0m(−1)i(mi)xk+m−i,
is considered. Under some conditions, the best constants An,m, and Bn,m are determined.