In this article we introduce the generalized lacunary difference sequence spaces [N
θ
,M,Δ
m
]0, [N
θ
,M,Δ
m
]1 and [N
θ
,M,Δ
m
]∞ using m
th
-difference. We study their properties like completeness, solidness, symmetricity. Also we obtain some inclusion relations
involving the spaces [N
θ
,M,Δ
m
]0,[N
θ
,M,Δ
m
]1 and [N
θ
,M,Δ
m
]∞ and the Cesàro summable and strongly Cesàro summable
... [Show full abstract] sequences.