On the Spaces of λr-almost Convergent and λr-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(lambda(r)) and f(0) (lambda(r)) 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 (lambda(r)). Finally, we give the characterization of some matrix classes.