Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2013 (2013), Article ID 247585, 7 pages.
A Generalized Nonlinear Sum-Difference Inequality of Product Form
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.
J. Appl. Math., Volume 2013 (2013), Article ID 247585, 7 pages.
First available in Project Euclid: 14 March 2014
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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