zbMATH — the first resource for mathematics

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)
Full Text:
References:
 [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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.