Journal of Inequalities and Applications
Volume 1 (1997), Issue 4, Pages 301-310

Discrete inequalities of Wirtinger’s type for higher differences

Gradimir V. Milovanović and Igor Ž. Milovanović

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.


Discrete version of Wirtinger’s type inequality for higher differences, An,mk=1nxk2k=lmum(Δmxk)2Bn,mk=1nxk2, where lm=1[m/2],um=n[m/2] and Δmxk=i=0m(1)i(mi)xk+mi, is considered. Under some conditions, the best constants An,m, and Bn,m are determined.