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

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_{۰}\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