Statistically convergent $\delta^{3}$ difference triple sequence spaces on a seminormed space
Resumo
In this paper we define and study the difference triple sequence spaces $\ell{\sf _{\infty st}^{3}(\Delta^{3},q)}$, \ ${\sfc_{st}^{3}(\Delta^{3},q)}$, \ ${\sf c_{st}^{3B}(\Delta^{3},q)}$, \${\sf c_{st}^{3R}(\Delta^{3},q)}$ and ${\sfc_{st}^{3BR}(\Delta^{3},q)}$} defined over a seminormed space $(X,q)$, seminormed by $q$. Some algebraic and topological properties of these classes of sequences are established and certain inclusion results have been obtained. Several examples are also provided to support the results and notions introduced.
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Referências
B. C. Das, A new type of difference operator Δ3 on triple sequence spaces, Proyecciones J. Math. 37(4), 683-697, (2018).
B. C. Das, Some I-convergent triple sequence spaces defined by a sequence of modulus function. Proyecciones J. Math.
(1), 117-130, (2017). .
B. C. Das, Six Dimensional Matrix Summability of Triple Sequences. Proyecciones J. Math. 36(3), 499-510, (2017).
B. C. Tripathy and A. Esi, A new type of difference sequence spaces. International J. Sci. Tech. 1(1), 11-14, (2006).
B. C. Tripathy and B. Sarma, Statistically convergent difference double sequence spaces. Acta Math.Sinica 24, 5, 737-742, (2008).
B. C. Tripathy and B. Sarma, Vector valued paranormed statistically convergent double sequence spaces. Math. Slovaca 57(2), 179-188, (2007).
B. C. Tripathy and R. Goswami, Vector valued multiple sequence spaces defined by Orlicz function. Bol. Soc. Paran. Mat. 33(1), 67-79, (2015).
B. C. Tripathy and R. Goswami , On triple difference sequences of real numbers in probabilistic normed spaces. Proyecciones Jour. Math. 33(2), 157-174, (2014).
B. C. Tripathy and R. Goswami, Multiple sequences in probabilistic normed spaces. Afrika Matematika 26(5-6), 753-760 (2015).
B. C. Tripathy and R. Goswami, Fuzzy real valued p-absolutely summable multiple sequences in probabilistic normed spaces. Afrika Matematika 26(7-8), 1281-1289, (2015).
B. C. Tripathy and R. Goswami, Statistically convergent multiple sequences in probabilistic normed spaces. U.P.B. Sci. Bull., Ser. A 78(4), 83-94 (2016).
B. C. Tripathy and M. Sen, Paranormed I-convergent double sequence spaces associated with multiplier sequences. Kyungpook Math. Journal 54(2), 321-332, (2014).
B. Das, B.C. Tripathy, P. Debnath and B. Bhattacharya, Almost convergence of complex uncertain triple sequences. Proc. Nat. Acad. Sci., Phy. Sci., https://doi.org/10.1007/s40010-020-00721-w
S. Debnath, B. C. Das, Some new type of difference triple sequence spaces. Palestine J. Math. 4(2), 284-290, (2015).
S. Debnath, B. C. Das, Some triple sequence spaces based on difference operator Δ2. Proceedings of ICFMGU 189-191, (2015).
S. Debnath, B. C. Das, D. Bhattacharya, J. Debnath, Regular matrix transformation on triple sequence spaces. Bol. Soc. Paran. Mat. 35(1), 85-96, (2017).
S. Debnath, B. Sharma, B.C. Das, Some generalized triple sequence spaces of real numbers. J. Nonlinear Anal. Optim. 6(1), 71-79, (2015).
G. Di Maio, Lj.D.R. Koˇcinac, Statistical convergence in topology. Topology Appl. 156(1), 28-45, (2008).
H. Fast, Sur la convergence statistique. Colloq. Math. 2, 241-244, (1951).
H. Kizmaz, On certain sequence spaces. Canad. Math. Bull. 24(2), 169–176,(1981).
M. Mursaleen, O.H.H. Edely, Statistical convergence of double sequences. J. Math. Anal. Appl. 288(1), 223-231, (2003).
H. H. Ostmann, Additive Zahlentheorie I, Springer-Verlag, Berlin-Gottingen-Heidelberg, 1956.
A. Pringsheim, Zur Theorie der zweifach unendlichen Zahlenfolgen. Math. Ann. 53(3), 289-321, (1900).
A. Sahiner, M. Gurdal, K. Duden, Triple sequences and their statistical convergence. Selcuk. J. Appl. Math. 8(2), 49-55, (2007).
E. Savas, A. Esi, Statistical convergence of triple sequences on probabilistic normed space. Annals Univ. Craiova, Math. Computer Sci. Ser. 39(2),226-236, (2012).
H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique. Colloq. Math. 2, 73-74, (1951).
O. Talo, Y. Sever, On statistical convergence of double sequences of closed sets, Filomat 30(3), 533-539, (2016).
O. Talo, Y. Sever, F. Basar, On statistically convergent sequences of closed sets, Filomat 30(6), 1497-1509, (2016).
B. C. Tripathy and B. Sarma, Vector valued paranormed statistically convergent double sequence spaces. Math. Slovaca 57(2), 179-188, (2007).
A. Zygmund, Trigonometric Series, 2nd edition, Cambridge University Press, Cambridge, (1979).
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