In [[12], Theorems 2.6-2.8] 2.6-2.8]te Pachpattethe following six discrete inequalities, based on which some new bounds on unknown functions are established.
First, we establish some new Volterra-Fredholm type discrete inequalities, based on which we derive explicit bounds for the solutions of Eq. (1) under some suitable conditions.
In this paper, we present some new discrete Volterra-Fredholm type inequalities, based on which we study the qualitative and quantitative properties of solutions of a class of Volterra-Fredholm type difference equation.
Based on the analysis above, in Section 2, we present some new Gronwall-type inequalities, based on which and some basic properties of the modified Riemann-Liouville fractional derivative, we derive explicit bounds for the unknown functions concerned in these inequalities.
A stable sufficient condition of the platoon of vehicles is given in terms of linear matrix inequalities (LMI), based on which the corresponding controller is also developed.
Some global exponential stability criteria are proposed in terms of linear matrix inequalities (LMIs), and based on which the procedure of impulsive controller design is proposed.
The following simple proof of the law of large numbers is based on Chebyshev's inequality, which illustrates the sense in which the variance of a distribution measures how the distribution is dispersed about its mean.
We have two systems an economic system, which is based on inequality, and a political system, which is based on equality.
In MIMO system, the power allocation for user-k in multi-cellular system should satisfy following inequality based on [5], which is under the equal allocation assumption.
These inequalities, which are based on classical convexity inequalities, generalize earlier inequalities for sums of operators.
