Six dimensional matrix summability of triple sequences.
Keywords:
Triple sequence, RH-regular, Regular matrix transformationAbstract
In this paper we introduced the RH-regularity condition of six dimensional matrix. Matrix summability is one of the important tool used to characterize sequence spaces. In 2004 Patterson presented such a characterization of bounded double sequence using four dimensional matrix. Our main aim is to extend Patterson result in triple sequence spaces using six dimensional matrix transformations.
References
A. Brudno, Summation of bounded sequences by matrices (in Russian), Recueil Math. (Mat. Sbornik), N.S. 16, pp. 191-247, (1945).
A. Pringsheim, Zurtheorie der zweifachunendlichenzahlenfolgen, Math. Ann. 53, pp. 289-321, (1900).
A. Sahiner, M. Gurdal and K. Duden, Triple sequences and their statistical convergence, Selcuk. J. Appl. Math., 8(2), pp. 49-55, (2007).
A. Sahiner, B. C. Tripathy, Some I-related properties of Triple sequences, Selcuk. J. Appl. Math., 9 (2), pp. 9-18, (2008).
B. C. Tripathy, R. Goswami, Vector valued multiple sequences defined by Orlicz functions, Bol. Soc. Paran. Mat., 33(1), pp. 67-79, (2015).
B. C. Tripathy, R. Goswami, Multiple sequences in probabilistic normed spaces, Afrika Matematika, 26(5-6), pp. 753-760, (2015).
B. C. Tripathy, R. Goswami, Fuzzy real valued p-absolutely summable multiple sequences in probabilistic normed spaces, Afrika Matematika, 26 (7-8), pp. 1281-1289, (2015).
B. C. Tripathy, R. Goswami, On triple difference sequences of real numbers in probabilistic normed spaces, Proyecciones J. Math., 33(2) , pp. 157-174, (2014).
B. C. Das, Some I-convergent triple sequence spaces defined by a sequence of modulus function, Proyecciones J. Math. (Accepted), (2017).
G. M. Robison, Divergent double sequences and series, Trans. Amer. Math. Soc., 28, pp. 50-73, (1926).
H. J. Hamilton, Transformations of multiple sequences, Duke Math. Jour., 2, pp. 29-60, (1936).
L. L. Silverman, On the definition of the sum of a divergent series, Ph. D. Thesis, University of Missouri Studies, Math. Series I, pp. 1- 96, (1913).
O. Toeplitz, Uber allgenmeine linear mittelbrildungen, Prace Mat. Fiz. (Warsaw) 22, (1911).
R. F. Patterson, Four dimensional characterization of bounded double sequences, Tamkang J. Math, 35(2), pp. 129-134, (2004).
S. Debnath, B. Sharma and B. C. Das, Some Generalized Triple Sequence Spaces of Real Numbers, J. Nonlinear Anal. Opti. 6(1), pp. 71-79, (2015).
S. Debnath and B. C. Das, Some New Type of Difference Triple Sequence Spaces, Palestine J. Math. Vol. 4(2), pp. 284-290, (2015).
S. Debnath, B. C. Das, D. Bhattacharya and J. Debnath, Regular Matrix Transformation on Triple Sequence Spaces, Bol. Soc. Paran. Mat., 35(1), pp. 85-96, (2017) (In Press).
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