A Generalized Nonlinear Sum-Difference Inequality of Product Form

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...

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Main Authors: YongZhou Qin, Wu-Sheng Wang
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/247585
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spelling doaj-ef46098c9fa44f208446559c4c7014472020-11-25T00:12:07ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/247585247585A Generalized Nonlinear Sum-Difference Inequality of Product FormYongZhou Qin0Wu-Sheng Wang1School of Mathematics and Statistics, Hechi University, Guangxi, Yizhou 546300, ChinaSchool of Mathematics and Statistics, Hechi University, Guangxi, Yizhou 546300, ChinaWe 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.http://dx.doi.org/10.1155/2013/247585
collection DOAJ
language English
format Article
sources DOAJ
author YongZhou Qin
Wu-Sheng Wang
spellingShingle YongZhou Qin
Wu-Sheng Wang
A Generalized Nonlinear Sum-Difference Inequality of Product Form
Journal of Applied Mathematics
author_facet YongZhou Qin
Wu-Sheng Wang
author_sort YongZhou Qin
title A Generalized Nonlinear Sum-Difference Inequality of Product Form
title_short A Generalized Nonlinear Sum-Difference Inequality of Product Form
title_full A Generalized Nonlinear Sum-Difference Inequality of Product Form
title_fullStr A Generalized Nonlinear Sum-Difference Inequality of Product Form
title_full_unstemmed A Generalized Nonlinear Sum-Difference Inequality of Product Form
title_sort generalized nonlinear sum-difference inequality of product form
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2013-01-01
description 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.
url http://dx.doi.org/10.1155/2013/247585
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AT wushengwang ageneralizednonlinearsumdifferenceinequalityofproductform
AT yongzhouqin generalizednonlinearsumdifferenceinequalityofproductform
AT wushengwang generalizednonlinearsumdifferenceinequalityofproductform
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