Pachpatte Inequalities on Time Scales

Some New Pachpatte Type Inequalities on Time Scales and Their Applications

The aim of this paper is to establish some new Pachpatte type inequalities on time scales, which provide explicit bounds on unknown functions. Our results extend some known Pachpatte inequalities on times scales, unify and extend some continuous inequalities and their corresponding discrete analogues. The inequalities given here can be used as tools in the qualitative theory of certain differen...

On Some Nonlinear Integral Inequalities on Time Scales

In this paper we study some nonlinear Pachpatte type integral inequalities on time scales by using a Bihari type inequality. Our results unify some continuous inequalities and their corresponding discrete analogues, and extend these inequalities to dynamic inequalities on time scales. Furthermore, we give some examples concerning our results.

Time Scales Inequalities

Here first we collect and develop necessary background on time scales required for this article. Then we present time scales integral inequalities of types: Poincaré, Sobolev, Opial, Ostrowski and Hilbert–Pachpatte. We give also the generalized analogs of all these inequalities involving high order delta derivatives of functions on time scales. We finish with lots of applications: all these ine...

Explicit Bounds to Some New Gronwall-Bellman-Type Delay Integral Inequalities in Two Independent Variables on Time Scales

Some new Gronwall-Bellman-type delay integral inequalities in two independent variables on time scales are established, which provide a handy tool in the research of qualitative and quantitative properties of solutions of delay dynamic equations on time scales. The established inequalities generalize some of the results in the work of Zhang and Meng 2008, Pachpatte 2002, and Ma 2010.

Some Pachpatte type inequalities on time scales