On H\`ajek - R\'enyi type inequality and application

Abstract

In this paper, we establish a new H\'ajek - R\'enyi's type inequality and obtain strong law of large numbers (SLLN) for arbitrary random variables. We base our methods on demimartingales and convex functions techniques. We obtain wide extensions of avalaible results, particularly those of Amini et al. and Rao and related SLLN's.