Four-dimensional generalized difference matrix and some double sequence spaces

In this study, I introduce some new double sequence spaces [Formula: see text] , [Formula: see text] , [Formula: see text] , [Formula: see text] and [Formula: see text] as the domain of four-dimensional generalized difference matrix [Formula: see text] in the spaces [Formula: see text] , [Formula: see text] , [Formula: see text] , [Formula: see text] and [Formula: see text] , respectively. I show that the double sequence spaces [Formula: see text] , [Formula: see text] and [Formula: see text] are the Banach spaces under some certain conditions. I give some inclusion relations with some topological properties. Moreover, I determine the α-dual of the spaces [Formula: see text] and [Formula: see text] , the [Formula: see text] -duals of the spaces [Formula: see text] , [Formula: see text] , [Formula: see text] , [Formula: see text] and [Formula: see text] , where [Formula: see text] , and the γ-dual of the spaces [Formula: see text] , [Formula: see text] and [Formula: see text] . Finally, I characterize the classes of four-dimensional matrix mappings defined on the spaces [Formula: see text] , [Formula: see text] , [Formula: see text] , [Formula: see text] and [Formula: see text] of double sequences.