Some Pachpatte type inequalities on time scales

Some Pachpatte type inequalities on time scales

Pachpatte Inequalities on Time Scales

In the study of dynamic equations on time scales we deal with certain dynamic inequalities which provide explicit bounds on the unknown functions and their derivatives. Most of the inequalities presented are of comparison or Gronwall type and, more specifically, of Pachpatte type.

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...

Some Opial-Type Inequalities on Time Scales

and Applied Analysis 3 where r t is positive and continuous function with ∫X a dt/r t < ∞, and if x b 0, then ∫b X |x t |∣∣x′ t ∣∣dt ≤ 1 2 ∫b

Some New Inequalities Similar to Hilbert-pachpatte Type Inequalities

In this paper, some new inequalities similar to Hilbert-Pachpatte type inequalities are given.