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Generalized Wijsman rough Weierstrass statistical six dimensional triple geometric difference sequence spaces of fractional order defined by Musielak-Orlicz function of interval numbers. (English) Zbl 1435.40002
From the summary: We generalize the concepts in probability of Wijsman rough lacunary statistical by introducing the interval numbers of Weierstrass of fractional order, where \({\alpha}\) is a proper fraction and \({\gamma} = ({\gamma}_{ mnk })\) is any fixed sequence of nonzero real or complex numbers. We study some properties of this operator involving Wijsman rough lacunary sequence \({\theta}\) of interval numbers and an arbitrary sequence \(p=(p_{rst})\) of strictly positive real numbers and investigate the topological structures of related six dimensional triple geometric difference sequence spaces of interval numbers.
MSC:
40A35 Ideal and statistical convergence
40J05 Summability in abstract structures (should also be assigned at least one other classification number from Section 40-XX)
40B05 Multiple sequences and series (should also be assigned at least one other classification number in this section)
46A45 Sequence spaces (including Köthe sequence spaces)
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[1] A. Esi, Statistical convergence of triple sequences in topological groups, Annals of the University of Craiova, Mathematics and Computer Science Series 40, 1 (2013), 29-33. Generalized Wijsman rough Weierstrass six dimensional geometric difference251 · Zbl 1299.40018
[2] A. Esi, On some triple almost lacunary sequence spaces defined by Orlicz func- tions, Research and Reviews: Discrete Mathematical Structures, 1, 2 (2014), 16-25.
[3] A. Esi and M. Necdet Catalbas, Almost convergence of triple sequences, Global J. Math. Anal., 2, 1 (2014), 6-10.
[4] A. Esi and E. Savas, On lacunary statistically convergent triple sequences in probabilistic normed space, Appl. Math. and Inf. Sci., 9, 5 (2015), 2529-2534.
[5] A. J. Dutta A. Esi and B.C. Tripathy, Statistically convergent triple sequence spaces defined by Orlicz function, J. Math. Anal., 4, 2 (2013), 16-22.
[6] S. Debnath, B. Sarma and B. C. Das, Some generalized triple sequence spaces of real numbers, J. Nonlinear Anal. Optimi., 6, 1 (2015), 71-79. · Zbl 1412.46009
[7] P. K. Kamthan and M. Gupta, Sequence spaces and series, Lecture notes, Pure and Applied Mathematics, 65 Marcel Dekker, In c. New York, 1981.
[8] J. Lindenstrauss and L. Tzafriri, On Orlicz sequence spaces, Israel J. Math., 10 (1971), 379-390. · Zbl 0227.46042
[9] J. Musielak, Orlicz Spaces, Lectures Notes in Math., 1034, Springer-Verlag, 1983.
[10] E. Savas and A. Esi, Statistical convergence of triple sequences on probabilistic normed space,of the University of Craiova, Mathematics and Computer Science Series, 39, 2 (2012), 226-236. · Zbl 1274.40035
[11] A. Sahiner, M. Gurdal and F. K. Duden, Triple sequences and their statistical convergence, Selcuk J. Appl. Math., 8, 2 (2007), 49-55. · Zbl 1152.40306
[12] A. Sahiner, B. C. Tripathy, Some I related properties of triple sequences, Selcuk J. Appl. Math., 9, 2 (2008), 9-18. · Zbl 1167.40300
[13] N. Subramanian and A. Esi, The generalized tripled difference of χ3sequence spaces, Global J. Math. Anal., 3, 2 (2015), 54-60.
[14] H. X. Phu, Rough convergence in normed linear spaces, Numerical Functional Analysis Optimization, 22 (2001), 201-224.
[15] S. Aytar, Rough statistical Convergence, Numerical Functional Analysis Optimization, 29, 3 (2008), 291-303. · Zbl 1159.40002
[16] S. K. Pal, D. Chandra and S. Dutta, Rough ideal Convergence, Hacee. Jounral Mathematics and Statistics, 42, 6 (2013), 633-640. · Zbl 1310.40007
[17] A. Esi and M. N. C¸ atalba¸s, Some sequence spaces of interval numbers defined by Orlicz functions, Proceedings of the Jangjeon Mathematical Society, 20, 1 (2017), 35-41.
[18] A. Esi, Strongly λ−summable sequences of interval numbers, International Journal of Science, Environment and Technology, 5, 6 (2016), 4643-4648.
[19] A. Esi, λ-Sequence spaces of interval numbers, Appl. Math. Inf. Sci., 8, 3 (2014), 1099-1102.
[20] A. Esi, A new class of interval numbers, Journal of Qafqaz University, Mathematics and Computer Science, 31 (2011), 98-102.
[21] A. Esi, Lacunary sequence spaces of interval numbers, Thai Journal of Mathematics 10, 2 (2012), 445-451. · Zbl 1261.40003
[22] A. Esi, Double lacunary sequence spaces of double sequence of interval numbers, Proyecciones Journal of Mathematics, 31, 1 (2012), 297-306. · Zbl 1263.46005
[23] A. Esi, Strongly almost λ-convergence and statistically almost λ-convergence of interval numbers, Scientia Magna, 7, 2 (2011), 117-122. 252N. Subramanian, A. Esi and M. K. Ozdemir
[24] A. Esi, Statistical and lacunary statistical convergence of interval numbers in topological groups, Acta Scientarium Technology, 36, 3 (2014), 491-495.
[25] A. Esi and N. Braha, On asymptotically λ-statistical equivalent sequences of in- terval numbers, Acta Scientarium Technology 35, 3 (2013), 515-520.
[26] A. Esi and A. Esi, Asymptotically lacunary statistically equivalent sequences of interval numbers, International Journal of Mathematics and Its Applications, 1, 1 (2013), 43-48.
[27] A. Esi and B. Hazarika, Some ideal convergence of double∧-interval number sequences defined by Orlicz function, Global Journal of Mathematical Analysis, 1, 3 (2013), 110-116.
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