engleski

On weighted discrete Hardy's inequality for negative power numbers

In this paper we consider the weighted discrete Hardy's inequality for different real power numbers $0 \neq r < 1$ and obtain some new refinements of its finite sections. For $r<-1$ our results improve those previously given by Nguyen et al. Moreover, we prove that the constant factors involved in the right-hand sides of the obtained inequalities are the best possible, that is, they cannot be replaced with any smaller constant.

strengthened discrete Hardy's inequality; negative power number; weights

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