In this paper, some new nonlinear generalized Gronwall-Bellman-Type integral inequalities with mixed time delays are established. These inequalities can be used as handy tools to research stability problems of delayed differential and integral dynamic systems. As applications, based on these new established inequalities, some p-stable results of a integro-differential equation are also given. T...

We present some new nonlinear integral inequalities Bellman-Bihari type with delay for discontinuous functions integro-sum inequalities; impulse integral inequalities . Some applications of the results are included: conditions of boundedness uniformly , stability by Lyapunov uniformly , practical stability by Chetaev uniformly for the solutions of impulsive differential and integrodifferential ...

Many Bayesian clinical trial methods are based on random inequalities. For some distribution families, these inequalities can be computed in closed form. For example, [1] gives closed-form solutions to computing P(X > Y) when X and Y are either independent normal or independent gamma random variables. However the case of beta random variables is very important and no closed form solution for th...

The paper deals with systems of hyperbolic differential-functional inequalities related to initial problem on the generalized Haar pyramid for equations ∂tzλ(t, x) = fλ(t, x, z, ∂xzλ(t, x)), λ ∈ Λ, where (t, x) = (t, x1, . . . , xn), z = {zλ}λ∈Λ and Λ is a compact set of indices. A theorem on strong differential-functional inequalities is the main result of the paper. Extremal solutions of init...

The theory of differential inequalities plays a central role in the qualitative and quantitative study of differential equations. In this paper, we present several comparison results for a class of functional differential equations of first order with periodic boundary value conditions. The inequalities obtained are, generally speaking, of the following type: Pv 5 0 implies that v 5 0, where P ...