Double sequence spaces defined by a modulus

Mathematica Slovaca

Ekrem Savaş¹  Richard Patterson¹ 

关键词: double sequences;    P-convergent;    modulus functions;   

DOI  :  10.2478/s12175-011-0009-2

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

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 $$mathop {sup }limits_{m,n} sumlimits_{k,l = 0,0}^{infty ,infty } {a_{m,n,k,l} < infty } $$ and let f be a modulus, then ω″(A, f) ⊂ ω″∞(A, f) and ω″0(A, f) ⊂ ω″∞(A, f).

【 授权许可】

Unknown