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Patterson, R. F. , Four Dimensional Characterization of Bounded Double Sequences, Tamkang J. Math. 35(2) (2004), 129–134. MR 2005d :40005 Patterson R. F. Four Dimensional

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statistical convergence of double sequences, Studia Sci. Math. Hungar. , 47 (1) (2010), 35–45. Coskun H. Double lacunary density and lacunary statistical convergence of double sequences

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Abstract  

We give a theorem of Vijayaraghavan type for summability methods for double sequences, which allows a conclusion from boundedness in a mean and a one-sided Tauberian condition to the boundedness of the sequence itself. We apply the result to certain power series methods for double sequences improving a recent Tauberian result by S. Baron and the author [4].

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] Das , Pratulananda , Malik , P. 2008 On the statistical and I variation of double sequences Real Anal. Exchange 33 351 – 364 . [5] Das , Pratulananda , Kostyrko , P. , Wilczyński

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Mursaleen and Osama H. Edely, Almost convergence and a core theorem for Double sequences (submitted). Patterson, R. F., Double sequence core theorems, Internat. J. Math. Math. Sci. 22

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Types of Sequential Equivalence , Kent State University, Mathematics. Patterson, R. F. , Some Characterization of Asymptotic Equivalent Double Sequences, International Journal of Mathematics and Mathematical

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Çakan, C. and Altay, B. , Statistically boundedness and statistical core of double sequences, J. Math. Anal. Appl. , 317 (2006), no. 2, 690–697. MR 2006k :40008

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Alotaibi , A.M. and Çakan , C., The Riesz convergence and Riesz core of double sequences, J. Inequal. Appl. , 2012 , 2012:56, 8 pp. Çakan C

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In this paper, necessary and sufficient conditions that the real doubly infinite matrixA sums every strongly almost convergent double sequence, leaving the limit invariant, have been determined.

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