On Some Properties of New Paranormed Sequence Space of Nonabsolute Type
نویسندگان
چکیده
and Applied Analysis 3 2. The Sequence Space λ, p In this section, we define the sequence space λ, p and prove that this sequence space according to its paranorm is complete paranormed linear space. In 1 , Mursaleen and Noman defined the matrix Λ λnk ∞ n,k 0 by λnk ⎧ ⎨ ⎩ λk − λk−1 λn 0 ≤ k ≤ n 0 k > n , 2.1 where λ λk ∞ k 0 is a strictly increasing sequence of positive reals tending to ∞, that is, 0 < λ0 < λ1 < · · · and λk → ∞ as k → ∞. Now, by using 2.1 we define new sequence space as follows: ( λ, p ) { x xk ∈ w : ∞ ∑
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