Meng, Fan Wei; Li, Wei Nian On some new nonlinear discrete inequalities and their applications. (English) Zbl 1032.26019 J. Comput. Appl. Math. 158, No. 2, 407-417 (2003). Summary: In this paper, some new discrete inequalities in two independent variables which provide explicit bounds on unknown functions are established. The inequalities given here can be used as handy tools in the qualitative theory of certain finite difference equations. Cited in 2 ReviewsCited in 21 Documents MSC: 26D15 Inequalities for sums, series and integrals 39A12 Discrete version of topics in analysis Keywords:discrete inequality; two independent variables; difference equation PDF BibTeX XML Cite \textit{F. W. Meng} and \textit{W. N. Li}, J. Comput. Appl. Math. 158, No. 2, 407--417 (2003; Zbl 1032.26019) Full Text: DOI OpenURL References: [1] Pachpatte, B.G., On certain new finite difference inequalities, Indian, J. pure appl. math., 24, 373-384, (1993) · Zbl 0788.26014 [2] Pachpatte, B.G., Some new finite difference inequalities, Comput. math. appl., 28, 227-241, (1994) · Zbl 0809.26009 [3] Pachpatte, B.G., On some new discrete inequalities useful in the theory of partial finite difference equations, Ann. differential equations, 12, 1-12, (1996) · Zbl 0864.26008 [4] Pachpatte, B.G., Inequalities applicable in the theory of finite difference equations, J. math. anal. appl., 222, 438-459, (1998) · Zbl 0913.39001 [5] B.G. Pachpatte, On some fundamental integral inequalities and their discrete analogues, J. Ineq. Pure Appl. Math. 2 (2001) Article 15. [ONLINE: http://jipam.vu.edu.au/] · Zbl 0989.26011 [6] Pachpatte, B.G., Inequalities for finite difference equations, (2002), Marcel Dekker New York · Zbl 0987.39001 [7] Yang, E.H., Generalizations of Pachpatte’s integral and discrete inequalities, Ann. differential equations, 13, 180-188, (1997) · Zbl 0885.34010 [8] Yang, E.H., A new integral inequality with power nonlinear and its discrete analogue, Acta math. appl. sinica, 17, 233-239, (2001) · Zbl 0987.26007 [9] Zhao, C.J., Some integral inequalities for differential equations, J. binzhou teachers college, 17, 4, 41-46, (2001), (in Chinese) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.