On the Spaces of $\lambda _{r}$-almost Convergent and $\lambda _{r}$-almost Bounded Sequences

Abstract

The aim of the present work is to introduce the concept of $\lambda _{r}$-almost convergence of sequences. We define the spaces $f\left( \lambda _{r}\right) $ and $f_{0}\left( \lambda _{r}\right) $ of $ \lambda _{r}$-almost convergent and $\lambda _{r}$-almost null sequences. We investigate some inclusion relations concerning those spaces with examples and we determine the $\beta $- and $\gamma $-duals of the space $f\left( \lambda _{r}\right) $. Finally, we give the characterization of some matrix classes.

Keywords

• almost convergence
• matrix domain
• $beta $-
• $gamma $-duals
• matrix transformations