On ?r-Convergence and ?r-Boundedness

Abstract

The aim of the present work is to introduce a new generalized concept of lambda-convergent and lambda-bounded sequences. We define new normed spaces related these sequences and construct their bases. We establish relationship between ordinary convergence and this new concept of convergence. We investigate some inclusion relations concerning with those spaces. Furthermore, the alpha-, beta- and gamma-duals of the new spaces are determined and some matrix classes are characterized.