Journal of Applied Mathematics

A Generalized Nonlinear Sum-Difference Inequality of Product Form

YongZhou Qin and Wu-Sheng Wang

Full-text: Open access

Abstract

We establish a generalized nonlinear discrete inequality of product form, which includes both nonconstant terms outside the sums and composite functions of nonlinear function and unknown function without assumption of monotonicity. Upper bound estimations of unknown functions are given by technique of change of variable, amplification method, difference and summation, inverse function, and the dialectical relationship between constants and variables. Using our result we can solve both the discrete inequality in Pachpatte (1995). Our result can be used as tools in the study of difference equations of product form.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 247585, 7 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808237

Digital Object Identifier
doi:10.1155/2013/247585

Mathematical Reviews number (MathSciNet)
MR3138927

Zentralblatt MATH identifier
06950580

Citation

Qin, YongZhou; Wang, Wu-Sheng. A Generalized Nonlinear Sum-Difference Inequality of Product Form. J. Appl. Math. 2013 (2013), Article ID 247585, 7 pages. doi:10.1155/2013/247585. https://projecteuclid.org/euclid.jam/1394808237


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