Abstract
In this paper, we define the sequence spaces: $\chi^{2qu}_{f\mu}\left(\Delta\right)$ and $\Lambda^{2qu}_{f\mu}\left(\Delta\right),$ where for any sequence $x=\left(x_{mn}\right),$ the difference sequence $\Delta x$ is given by $\left(\Delta x_{mn}\right)_{m,n=1}^{\infty}=\left[\left(x_{mn}-x_{mn+1}\right)-\left(x_{m+1n}-x_{m+1n+1}\right)\right]_{m,n=1}^{\infty}.$ We also study some properties and theorems of these spaces.
Highlights
Colak [8,9] have proved that Mu (t) and Cp (t), Cbp (t) are complete paranormed spaces of double sequences and gave the α−, β−, γ− duals of the spaces Mu (t) and Cbp (t)
The class of sequences which are strongly Cesaro summable with respect to a modulus was introduced by Maddox [18] as an extension of the definition of strongly
We introduce the following difference double sequence spaces defined by
Summary
We introduce the following difference double sequence spaces defined by. The notion of λ− double gai and double analytic sequences as follows: Let λ = (λmn)∞ m,n=0 be a strictly increasing sequences of positive real numbers tending to infinity, that is 0 < λ00 < λ11 < · · · and λmn → ∞ as m, n → ∞. Let f = (fmn) be a Musielak-modulus function and ( X, (d (x1) , d (x2) , · · · , d (xn−1)) p be a p−metric space, q = (qmn) be double analytic sequence of strictly positive real numbers and u = (umn) be any sequence such that umn = 0 (m, n = 1, 2, · · · ). In the present paper we define the following sequence spaces: χ2fqμu ,.
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