Let $A = (a_{n,k})$ and $B = (b_{n,k})$ be two infinite matrices with real entries. The main purpose of this paper is to generalize the multiplier space for introducing the concepts of αAB-, βAB-, γAB-duals and NAB-duals. Moreover, these duals are investigated for the sequence spaces X and X(A), where $X \in \{c_0 , c, l_p }$ for $1 \le p \le \infty$. The other purpose of the present study is to introduce the sequence spaces $$X(A,\Delta) = eft \{x= (x_k)\colon eft(um_{k=1}^ıfty a_{n,k} x_k - um_{k=1}^ıfty a_{n-1,k} x_k\right )_{n=1}^ıfty ı X \right\},$$ where $X \in \{l_\infty, c, c_0\}$, and computing the NAB-(or Null) duals and $\beta AB$-duals for these spaces.