On some new sequence spaces of non-absolute type related to the spaces ℓp and ℓ∞ I

Abstract

In the present paper, we introduce the sequence space λ p of non-absolute type and prove that the spaces λ p and p are linearly isomorphic for 0 < p ≤ ∞. Further, we show that λ p is a p-normed space and a BK-space in the cases of 0 < p < 1 and 1 ≤ p ≤ ∞, respectively. Furthermore, we derive some inclusion relations concerning the space λ p. Finally, we construct the basis for the space λ p , where 1 ≤ p < ∞.

Survey on the domain of the matrix lambda in the normed and paranormed sequence spaces

“…Mursaleen and Noman [36,40,41] prove the following theorem concerning the inclusion relations between these spaces and the classical sequence spaces`1, c and c 0 : The alpha-, beta-and gamma-duals of the spaces` 1 , c and c 0 are determined. Some matrix transformations on these spaces are also characterized.…”

Matrix transformation of Fibonacci band matrix on generalized $bv$-space and its dual spaces

“…We refer [9,12,14,15,17] for the concept of matrix transformations. Now, we may give the following lemma due to Stieglitz and Tietz [11] on the characterization of the matrix transformations between some sequence spaces.…”

Orlicz strongly convergent sequences with some applications to Fourier series and statistical convergence

“…Mursaleen and Noman [20] introduced the notion of λ -convergent and λ -bounded sequences. Let λ = {λ k } ∞ k=0 be a strictly increasing sequence of positive real numbers tending to infinity.…”