The Cesáro Core of Double Sequences
نویسندگان
چکیده
and Applied Analysis 3 where σ s σ σj−1 s . In this case, we write σ − limx . By V 2 σ , we denote the set of all σ-convergent and bounded double sequences. One can see that in contrast to the case for single sequences, a convergent double sequence need not be σ-convergent. But every bounded convergent double sequence is σ-convergent. So, c∞ 2 ⊂ V 2 σ ⊂ ∞ 2 . In the case σ i i 1, σ-convergence of double sequences reduces to the almost convergence. A matrix A a jk j,k 0 is said to be σ-regular if Ax ∈ V σ 2 for x xjk ∈ c∞ 2 with σ − limAx limx, and we denote this by A ∈ c∞ 2 , V σ 2 reg, see 5, 6 . Mursaleen and Mohiuddine defined and characterized σ-conservative and σ-coercive matrices for double sequences 6 . A double sequence x xjk of real numbers is said to be Cesáro convergent or C1convergent to a number L if and only if x ∈ C1, where C1 { x ∈ ∞ 2 : lim p,q→∞pq x L;L C1 − limx } , Tpq x 1 ( p 1 )( q 1 ) p ∑
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تاریخ انتشار 2014