Rubio de Francia Extrapolation Theorem for Quasi non-increasing Sequences

We prove the discrete Rubio de Francia extrapolation theorem for a pair of quasi non-increasing sequences with ${\mathcal{Q}\mathcal{B}}_{\beta ,p}$ weight class. Also, a weight characterization of the boundedness of the generalized discrete Hardy averagin19g operator on the class of quasi non-increasing sequences from $l_w^p({\mathbb{Z}}^{+})$ is proved.