On the Difference Sequence Space `p(Tˆq)

Özet

In this study, we introduce a new matrix Tˆq = (tˆ q nk) by tˆ q nk =    qn Qn tn , k = n qk Qn tk − qk+1 Qn 1 tk+1 , k n. where tk > 0 for all n ∈ N and (tn) ∈ c\c0. By using the matrix Tˆq , we introduce the sequence space `p(Tˆq ) for 1 ≤ p ≤ ∞. In addition, we give some theorems on inclusion relations associated with `p(Tˆq ) and find the α-, β-, γ- duals of this space. Lastly, we analyze the necessary and sufficient conditions for an infinite matrix to be in the classes (`p(Tˆq ), λ) or (λ, `p(Tˆq )), where λ ∈ {`1, c0, c, `∞}.