A new type of difference operator Δ3 on triple sequence spaces.
Keywords:
Triple sequence space, difference operator, solidity, symmetricityAbstract
In this paper we have introduced and investigated the difference triple sequence spaces c³0(Δ³), c³(Δ³), c³R(Δ³), ?³∞(Δ³) and c³B(Δ³) applying the difference operator Δ³, on the triple sequence (xlmn) and studied some of their algebraic and topological properties. We have also proved some inclusion relation involving these sequence spaces.
References
A. Esi, Some new sequence spaces defined by a modulus function, Istanbul Univ Fen Fak Mat Derg., 55/56: pp. 17-21, (1996/97).
A. Esi and B. C. Tripathy, Strongly almost convergent generalized difference sequences associated with multiplier sequences, Math. Slovaca, 57(4), pp. 339-348, (2007).
A. J. Datta, A. Esi , B. C. Tripathy , Statistically convergent triple sequence spaces defined by Orlicz function, J. Math. Anal., 4(2), pp. 16-22, (2013).
A. Sahiner, M. Gurdal and K. Duden, Triple sequences and their statistical convergence, Selcuk. J. Appl. Math., 8(2), pp. 49-55, (2007).
A. Pringsheim, Zurtheorie der zweifachunendlichenzahlenfolgen, Math. Ann., 53, pp. 289-321, (1900).
B. C. Das, Some I-convergent triple sequence spaces defined by a sequence of modulus function, Proyecciones J. Math., 36(1), pp. 117-130, (2017).
B. C. Das, Six Dimensional Matrix Summability of Triple Sequences, Proyecciones J. Math. , 36(3), pp. 499-510, (2017).
B. C. Tripathy , On generalized difference paranormed statistically convergent sequences, Indian J. Pure Appl. Math., 35 (5), pp. 655-663, (2004).
B. C. Tripathy and B. Sarma, Statistically convergent difference double sequence spaces, Acta Math. Sinica, 24(5), pp. 737-742, (2008).
B. C. Tripathy , B. Choudhary andB. Sarma. , On some new type generalized difference sequence spaces, Kyungpook Math. J., 48(4), pp. 613-622, (2008).
B. C. Tripathy and H. Dutta., On some new paranormed difference sequence spaces defined by Orlicz functions, Kyungpook Math. J. , 50(1), pp. 59-69, (2010).
B. C. Tripathy andH. Dutta., On some lacunary difference sequence spaces defined by a sequence of Orlicz functions and q-lacunary Δn m- statistical convergence, Analele Stiintifice ale Universitatii Ovidius, Seria Matematica, 20(1), pp. 417-430, (2012).
B. C. Tripathy and R. Goswami., On triple difference sequences of real numbers in probabilistic normed spaces, Proyecciones Jour. Math., 33(2), pp. 157-174, (2014).
E. Savas and R. F. Patterson , Double Sequece Spaces Defined by a Modulus, Math. Slovaca , 61, pp. 245-256, (2011).
E. Saves andA. Esi , Statistical Convergence of Triple Sequences on Probabilistic Normed Spaces, An. Univ. Craiova Ser. Mat. Inform., 39(2), pp. 226-236, (2012).
H. Kizmaz, On certain sequence spaces, Canad. Math. Bull., 24(2), pp. 169-176, (1981).
I. J. Maddox, Sequece Spaces Defined by a Modulus, Math. Proc. Cambridge Philos. Soc., 100, pp. 161-166, (1986).
M. Et andA. Esi , On Kothe-Toeplitz duals of generalized difference Sequence Spaces, Bul. Malaysian Math. Sci. Soc., (Second Series), 23, pp. 1-8, (2000).
M. Et and R. Colak, On some generalized difference sequence spaces, Soochow J. Math., 21, pp. 377-386, (1995).
S. Debnath, B. C. Das, Some new type of difference triple sequence spaces, Palestine J. Math., 4 (2), pp. 284-290, (2015).
S. Debnath , B. Sharma, B. C. Das , Some generalized triple sequence spaces of real numbers, J. Nonlinear Anal. Opti., 6 (1), pp. 71-79,(2015).
S. Debnath , B. C. Das , D. Bhattacharya, J. Debnath, Regular matrix transformation on triple sequence spaces. Bol. Soc. Paran. Mat., 35 (1), pp. 85-96, (2017).
W. H. Ruckle, On perfect Symmetric BK-spaces, Math. Ann. , 175, pp. 121-126, (1968)
Published
How to Cite
Issue
Section
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.