On the Spaces of λr-almost Convergent and λr-almost Bounded Sequences

The aim of the present work is to introduce the concept of λr-almost convergence of sequences. We define the spaces f (λr) and f0 (λr) of λr-almost convergent and λr-almost null sequences. We investigate some inclusion relations concerning those spaces with examples and we determine the β- and γ-duals of the space f (λr). Finally, we give the characterization of some matrix classes.