Abstract
Abstract In the present paper we introduce double sequence space m 2 ( M , A , ϕ , p , ∥ ⋅ , … , ⋅ ∥ ) defined by a sequence of Orlicz functions over n-normed space. We examine some of its topological properties and establish some inclusion relations. MSC:40A05, 46A45.
Highlights
Introduction and preliminariesThe initial works on double sequences is found in Bromwich [ ]
Mursaleen and Edely [ ] have recently introduced the statistical convergence which was further studied in locally solid Riesz spaces [ ]
Altay and Başar [ ] have defined the spaces BS, BS(t), CSp, CSbp, CSr and BV of double sequences consisting of all double series whose sequence of partial sums are in the spaces Mu, Mu(t), Cp, Cbp, Cr and Lu, respectively and examined some properties of these sequence spaces and determined the α-duals of the spaces BS, BV, CSbp and the β(v)-duals of the spaces CSbp and CSr of double series
Summary
Introduction and preliminariesThe initial works on double sequences is found in Bromwich [ ]. Besides {φk,l} is taken as a non-decreasing double sequence of the positive real numbers such that kφk+ ,l ≤ (k + )φk,l, lφk,l+ ≤ (l + )φk,l. Lindenstrauss and Tzafriri [ ] used the idea of Orlicz function to define the following sequence space: M= |xk | ρ which is called an Orlicz sequence space.
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