Abstract
In this work we introduce new spaces m2(F,ϕ,p) of double sequences defined by a double sequence of modulus functions, and we study some properties of this space.
Highlights
By w and w2, we denote the spaces of single complex sequences and double complex sequences, respectively
A double sequence space E is said to be symmetric if u = ∈ E and ‖u‖ = ‖x‖ whenever x = ∈ E and u ∈ S(x)
In this work we introduce sequence spaces m2(F, φ, p) defined by m2 (F, φ, p) sup (s,t)≥(1,1)
Summary
By w and w2, we denote the spaces of single complex sequences and double complex sequences, respectively. A real double sequence {xk,l} is nondecreasing, if xk,l ≤ xp,q for (k, l) < (p, q). For 1 ≤ p < ∞, lp(2) denote the space of sequences x = {xk,l} such that k,l=1 (see [4]). A double sequence x = {xk,l} is said to be bounded if and only if supk,l|xk,l| < ∞.
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