University of MaraghehSahand Communications in Mathematical Analysis2322-580717320200701On the Spaces of $lambda _{r}$-almost Convergent and $lambda _{r}$-almost Bounded Sequences1171304057910.22130/scma.2019.111716.644ENSinanErcanDepartment of Mathematics, Faculty of Science, Firat University, 23119, Elazig, Turkey.0000-0001-9871-2142Journal Article20190721The aim of the present work is to introduce the concept of $lambda _{r}$-almost convergence of sequences. We define the spaces $fleft( 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 $fleft( lambda _{r}right) $. Finally, we give the characterization of some matrix classes.http://scma.maragheh.ac.ir/article_40579_85759bdb155dcfb274e7ac69b0e053fb.pdf