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

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

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.