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International Journal of Mathematics and Mathematical Sciences
Volume 9, Issue 3, Pages 485-495

On some new N-independent-variable discrete inequalities of the Gronwall type

Department of Mathematics, Jinan University, Guang Zhou, China

Received 26 June 1985

Copyright © 1986 Hindawi Publishing Corporation. 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.


In this paper we shall establish some new discrete inequalities of the Gronwall type in N-independent variables. They will have many applications for finite difference equations involving several independent variables and for numerical analysis. Their consequence for the case of N=3, generalizes all of the known theorems obtained by Pachpatte and Singare in [1]. An example, to which those results established in [1] are inapplicable, is given here to convey the usefulness of the results obtained.