On Generalized Difference Double Sequence Space Defined over Class of p-Supremum Bounded Variation Double Sequences

摘要

Recently, the monotone decreasing coefficients of sine series has been generalized by classes of general monotone sequences. Further, class of general monotone sequences can be generalized by classes of p-supremum bounded variation sequences and p-supremum bounded variation double sequences. By considering the definition of p-supremum bounded variation sequences is a summing the difference sequence of the first order, then this summation can be extended to summation of the nth order. Furthermore, in the double sequence, the difference the first order can be extended to the nth order. In this paper we define the generalized difference double sequence by class of p-supremum bounded variation double sequences. It will be proved that this class is separable Banach space.