Double sequence spaces defined by a modulus |
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| Authors: | Ekrem Savaş Richard F Patterson |
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| Institution: | (1) Department of Mathematics, Firat University, 23119 Elazig, Turkey;(2) Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India |
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| Abstract: | 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
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$
\mathop {\sup }\limits_{m,n} \sum\limits_{k,l = 0,0}^{\infty ,\infty } {a_{m,n,k,l} < \infty }
$
\mathop {\sup }\limits_{m,n} \sum\limits_{k,l = 0,0}^{\infty ,\infty } {a_{m,n,k,l} < \infty }
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| Keywords: | |
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