In this paper we introduce a general seguence space Av(X) = .[s = (xjj): (vj^X|^ — k+ı X|j4.,) e X}, wlıere X is any sequence space. We establish some inclusion relations, topological results, in general case and we characterize the continuons, a-, p- andy- duals of Av(X) for varions seguence spaces X. The results of this paper, in a particular case, incinde the corresponding results of KIZMAZ.