Difference sequence spaces derived by using a generalized weighted mean

In this work, we define new sequence spaces by combining a generalized weighted mean and a difference operator. Afterward, we investigate topological structures, which have completeness, A K -property, and A D -property. Also, we compute the α -, β - and γ -duals, and obtain bases for these sequence spaces. Finally, the necessary and sufficient conditions on an infinite matrix belonging to the classes ( c ( u , v , Δ ) : ℓ ∞ ) and ( c ( u , v , Δ ) : c ) are obtained.