%0 Journal Article %T On the Spaces of $\lambda _{r}$-almost Convergent and $\lambda _{r}$-almost Bounded Sequences %J Sahand Communications in Mathematical Analysis %I University of Maragheh %Z 2322-5807 %A Ercan, Sinan %D 2020 %\ 07/01/2020 %V 17 %N 3 %P 117-130 %! On the Spaces of $\lambda _{r}$-almost Convergent and $\lambda _{r}$-almost Bounded Sequences %K Almost convergence %K Matrix domain %K $beta $- %K $gamma $-duals %K Matrix transformations %R 10.22130/scma.2019.111716.644 %X 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. %U https://scma.maragheh.ac.ir/article_40579_066143a7d10937a4e6abbbf977cc82f6.pdf