Some new maximal inequalities

some maximal inequalities for random variables and applications

in this paper, we extend some famous maximal inequalities and obtain strong laws of largenumbers for arbitrary random variables by use of these inequalities and martingale techniques.

Some New Hilbert’s Type Inequalities

Some New Hilbert-pachpatte’s Inequalities

Some new Hilbert-Pachpatte discrete inequalities and their integral analogues are established in this paper. Other inequalities are also given in remarks.

Some New Iyengar Type Inequalities

Some new Iyengar type inequalities for an integral are obtained by using the generalised Taylor formula with integral remainder.

On Some Maximal Inequalities for Demisubmartingales and N−demisuper Martingales

We study maximal inequalities for demisubmartingales and N-demisupermartingales and obtain inequalities between dominated demisubmartingales. A sequence of partial sums of zero mean associated random variables is an example of a demimartingale and a sequence of partial sums of zero mean negatively associated random variables is an example of a Ndemimartingale.