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The riesz convergence and riesz core of double sequences
(Springeropen, 2012) Alotaibi, Abdullah M.; Cakan, Celal
In this article, we have introduced the Riesz convergence and Riesz core of double sequences and determined the necessary and sufficient conditions on a four-dimensional matrix A to yield P-R - core{Ax}. P subset of core{x} and P-R - core{Ax} subset of st(2) - core {x} for all x is an element of l(infinity)(2).
The Riesz Core of a Sequence
(Gazi Univ, 2011) Cakan, Celal; Alotaibi, Abdullah M.
The Riesz sequence space r(c)(q) including the space c has recently been defined in [14] and its some properties have been investigated. In the present paper, we introduce a new type core, K-q-core, of a complex valued sequence and also determine the required conditions for a matrix B for which K-q-core (Bx) subset of K-core (x), K(q)core (Bx) subset of st(A)-core (x) and K-q-core (Bx) subset of K-q-core (x) hold for all x is an element of l(infinity).