Double sequence spaces defined by a modulus

In: Mathematica Slovaca, vol. 61, no. 2

Ekrem Savaş - Richard F. Patterson

Detaily:

Rok, strany: 2011, 245 - 256

Kľúčové slová:

double sequences, P-convergent, modulus functions

DOI: https://doi.org/10.2478/s12175-011-0009-2

O článku:

This paper begins with new definitions for double sequence spaces. These new definitions are constructed, in general, by combining modulus function and nonnegative four-dimensional matrix. We use these definitions to establish inclusion theorems between various sequence spaces such as: If $A=(a_m,n,k,l)$ be a nonnegative four-dimensional matrix such that

$$ \sup_m,n∑_k,l=0,0^∞,∞a_m,n,k,l<∞ $$

and let $f$ be a modulus, then $ω''(A,f)\subset ω_∞''(A,f)$ and $ω''₀(A,f)\subset ω_∞''(A,f)$.

Ako citovať:

ISO 690:

Savaş, E., Patterson, R. 2011. Double sequence spaces defined by a modulus. In Mathematica Slovaca, vol. 61, no.2, pp. 245-256. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0009-2

APA:

Savaş, E., Patterson, R. (2011). Double sequence spaces defined by a modulus. Mathematica Slovaca, 61(2), 245-256. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0009-2

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