Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter May 23, 2020

On sequence spaces defined by the domain of a regular tribonacci matrix

  • Taja Yaying and Bipan Hazarika EMAIL logo
From the journal Mathematica Slovaca

Abstract

In this article we introduce Tribonacci sequence spaces p(T) (1 ≤ p ≤ ∞) derived by the domain of a newly defined regular Tribonacci matrix. We give some topological properties, inclusion relation, obtain the Schauder basis and determine the α-, β- and γ-duals of the new spaces. We characterize the matrix classes on p(T). Finally, we give some geometric properties of the space p(T).



  1. Communicated by Gregor Dolinar

References

[1] Alotaibi, M.—Mursaleen, M.—Alamri, B.—Mohiuddine, S. A.: Compact operators on some Fibonacci difference sequence spaces, J. Inequal. Appl. 203 (2015), 8 pp.10.1186/s13660-015-0713-5Search in Google Scholar

[2] Altay, B.—Başar, F.—Mursaleen, M.: On the Euler sequence spaces which include the spaces ℓp and ℓ I., Inf. Sci. 176 (2006), 1450–1462.10.1016/j.ins.2005.05.008Search in Google Scholar

[3] Başarir, M.—Başar, F.—Kara, E. E.: On the spaces of Fibonacci difference absolutely p-summable, null and convergent sequences, Sarajevo J. Math. 12(25) (2016), 167–182.10.5644/SJM.12.2.04Search in Google Scholar

[4] Bruce, I.: A modified Tribonacci sequence, Fibonacci Quart. 22(1984), 244–246.Search in Google Scholar

[5] Candan, M.: A new approach on the spaces of generalized Fibonacci difference null and convergent sequences, Math. Aeterna 5(1) (2015), 191–210.Search in Google Scholar

[6] Catalani, M.: Identities for Tribonacci-related sequences, arXiv:math/0209179 [math.CO].Search in Google Scholar

[7] Chandra, P.—Tripathy, B. C.: On generalised Köthe-Toeplitz duals of some sequence spaces, Indian J. Pure Appl. Math. 33 (2002), 1301–1306.Search in Google Scholar

[8] Choi, E.: Modular Tribonacci numbers by matrix method, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math. 20 (2013), 207–221.10.7468/jksmeb.2013.20.3.207Search in Google Scholar

[9] Clarkson, J. A.: Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), 396–414.10.1090/S0002-9947-1936-1501880-4Search in Google Scholar

[10] Das, A.—Hazarika, B.: Some new Fibonacci difference spaces of non-absolute type and compact operators, Linear Multilinear Algebra 65(12) (2017), 2551–2573.10.1080/03081087.2017.1278738Search in Google Scholar

[11] Debnath, S.—Saha, S.: Some newly defined sequence spaces using regular matrix of Fibonacci numbers, AKU J. Sci. Eng. 14 (2014), 1–3.10.5578/fmbd.6907Search in Google Scholar

[12] Devbhadra, S. V.: Some Tribonacci identities, Math. Today 27 (2011), 1–9.Search in Google Scholar

[13] Ercan, S.— Bektaş, C. A.: Some topological and geometric properties of a new BK-space derived by using regular matrix of Fibonacci numbers, Linear Multilinear Algebra 65(5) (2017), 909–921.10.1080/03081087.2016.1215403Search in Google Scholar

[14] Feinberg, M.: Fibonacci–Tribonacci, Fibonacci Quart. 1 (1963), 71–74.Search in Google Scholar

[15] Howard, F. T.: A Tribonacci Identity, Fibonacci Quart. 39 (2001), 352–357.Search in Google Scholar

[16] Jarrah, A. M.—Malkowsky, E.: Ordinary, absolute and strong summability and matrix transformations, Filomat 17 (2003), 59–78.10.2298/FIL0317059JSearch in Google Scholar

[17] Kara, E. E.: Some topological and geometric properties of new Banach sequence spaces, J. Inequal. Appl. 38 (2013), 15 pp.10.1186/1029-242X-2013-38Search in Google Scholar

[18] Kara, E. E.—Ilkhan, M.: On some Banach sequence spaces derived by a new band matrix, British J. Math. Comput. Sci. 9 (2015), 141–159.10.9734/BJMCS/2015/17499Search in Google Scholar

[19] Kara, E. E.—Ilkhan, M.: Some properties of generalized Fibonacci sequence spaces, Linear Multilinear Algebra 64(11) (2016), 2208–2223.10.1080/03081087.2016.1145626Search in Google Scholar

[20] Kara, E. E.—Demiriz, S.: Some new paranormed difference sequence spaces derived by Fibonacci numbers, Miskolc Math. Notes 16(2) (2015), 907–923.10.18514/MMN.2015.1227Search in Google Scholar

[21] Kesavan, S.: Functional Analysis, New Delhi, Hindustan, 2009.10.1007/978-93-86279-42-2Search in Google Scholar

[22] Kirişç, M.—Başar, F.: Some new sequence spaces derived the domain of generalized difference matrix, Comput. Math. Appl. 60 (2010), 1299–1309.10.1016/j.camwa.2010.06.010Search in Google Scholar

[23] Kiliç, E.: Tribonacci sequences with certain indices and their sums, Ars. Comb. 86 (2008), 13–22.Search in Google Scholar

[24] Koshy, T.: Fibonacci and Lucus Numbers with Applications, Wiley, New York (2001).10.1002/9781118033067Search in Google Scholar

[25] Köthe, G.—toeplitz, O.: Linear Raume mit unendlich vielen Koordinaten and Ringe unenlicher Matrizen, J. Reine Angew. Math. 171 (1934), 193–226.10.1515/crll.1934.171.193Search in Google Scholar

[26] Malkowsky, E.—Rakočević, V.: On matrix domains of triangles, Appl. Math. Comput. 189 (2007), 1146–1163.10.1016/j.amc.2006.12.024Search in Google Scholar

[27] Mursaleen, M.—Başar, M.—Altay, B.: On the Euler sequence spaces which include the spaces ℓp and ℓ II, Nonlinear Anal. 65(3) (2006), 707–717.10.1016/j.na.2005.09.038Search in Google Scholar

[28] Pethe, S.: Some identities for Tribonacci sequences, Fibonacci Quart. 26 (1988), 144–151.Search in Google Scholar

[29] Pettis, B. J.: A proof that every uniformly convex space is reflexive, Duke Math. J. 5(2) (1939), 249–253.10.1215/S0012-7094-39-00522-3Search in Google Scholar

[30] Scott, A.—Delaney, T.—Hoggatt JR, V.: The Tribonacci sequence, Fibonacci Quart. 15 (1977), 193–200.Search in Google Scholar

[31] Spickerman, W.: Binet’s formula for the Tribonacci sequence, Fibonacci Quart. 20 (1982), 118–120.Search in Google Scholar

[32] Stieglitz, M.—Tietz, H.: Matrixtransformationen von Folgenräumen eine Ergebnisübersicht, Math. Z. 154 (1977), 1–16.10.1007/BF01215107Search in Google Scholar

[33] Tripathy, B. C.: Matrix transformations between some classes of sequences, J. Math. Anal Appl. 206(3) (1997), 448–450.10.1006/jmaa.1997.5236Search in Google Scholar

[34] Tripathy, B. C.—Sen, M.: Characterization of some matrix classes involving paranormed sequence spaces, Tamkang J. Math. 37(2) (2006), 155–162.10.5556/j.tkjm.37.2006.160Search in Google Scholar

[35] Wilansky, A.: Summability through Functional Analysis. North-Holland Mathematics Studies, vol. 85, Elsevier, Amsterdam, 1984.Search in Google Scholar

[36] Yalavigi, C. C.: Properties of Tribonacci numbers, Fibonacci Quart. 10 (1972), 231–246.Search in Google Scholar

Received: 2019-03-09
Accepted: 2019-11-26
Published Online: 2020-05-23
Published in Print: 2020-06-25

© 2020 Mathematical Institute Slovak Academy of Sciences

Downloaded on 18.4.2024 from https://www.degruyter.com/document/doi/10.1515/ms-2017-0383/html
Scroll to top button