A New Paranormed Sequence Space Defined by Regular Bell Matrix

Authors

DOI:

https://doi.org/10.56405/dngcrj.2023.08.01.03

Keywords:

Bell numbers, Paranormed sequence space, Matrix transformation, α-,β-,γ-duals

Abstract

This paper aims to construct a new paranormed sequence space by the aid of a regular matrix of Bell numbers. As well, its special duals such as α−,β−,γ−  duals are presented and Schauder basis is determined. Moreover, certain matrix classes for this space are characterized. 

Downloads

Download data is not yet available.

References

Alp, P.Z. (2020). A new paranormed sequence space defined by Catalan conservative matrix. Mathematical Methods in Applied Sciences, 44 (9), 7651–7658.

Altay, B., Başar, F. (2006). Some paranormed sequence spaces of non-absolute type derived by weighted mean. Journal of Mathematical Analysis and Applied Mathematics, 319 (2), 494–508.

Aydın, C., Başar, F. (2004). Some new paranormed sequence spaces. Information Sciences, 160 (1-4), 27–40.

Candan, M. (2012). Domain of the double sequential band matrix in the classical sequence spaces. Journal of Inequalities and Applications, 2012, 281.

Candan, M., Güneş, A. (2015). Paranormed sequence space of non-absolute type founded using generalized difference matrix. Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 85 (2), 269–276.

Choudhary, B., Mishra, S.K. (1993). On Köthe-Toeplitz duals of certain sequence spaces and their matrix transformations. Indian Journal of Pure and Applied Mathematics, 24 (5), 291–301.

Dağlı, M.C. (2023). On the paranormed sequence space arising from Catalan–Motzkin matrix. Advances in Operator Theory, 8 (2), 33.

Dağlı, M.C., Yaying, T. (2023). Some new paranormed sequence spaces derived by regular Tribonacci matrix. The Journal of Analysis, 31, 109–127.

Et, M., Çolak, R. (1995). On some generalized difference sequence spaces. Soochow Journal of Mathematics, 21 (4), 377–386.

Grosseerdmann, K.G. (1993). Matrix transformations between the sequence spaces of Maddox. Journal of Mathematical Analysis and Applications, 180 (1), 223–238.

İlkhan, M., Kara, E.E., Usta, F. (2020). Compact operators on the Jordan totient sequence spaces. Mathematical Methods in Applied Sciences, 44 (9), 7666–7675.

İlkhan, M., Simsek, N., Kara, E.E. (2020). A new regular infinite matrix defined by Jordan totient function and its matrix domain in . Mathematical Methods in Applied Sciences, 44 (9), 7622–7633.

İlkhan, M., Demiriz, S., Kara, E.E. (2019). A new paranormed sequence space defined by Euler totient matrix. Karaelmas Science and Engineering Journal, 9 (2), 277–282.

Kara E.E., Demiriz, S. (2015). Some new paranormed difference sequence spaces derived by Fibonacci numbers. Miskolc Mathematical Notes, 16 (2), 907–923.

Karakas, M. (2023). On the sequence spaces involving bell numbers. Linear and Multilinear Algebra, 71 (14), 2298-2309.

Karakaya, V., Noman, A.K., Polat, H. (2011). On paranormed sequence spaces of non-absolute type. Mathematical and Computer Modelling, 54, 1473–1480.

Karakaya, V., Savaş, E., Polat, H. (2013). Some paranormed Euler sequence spaces of difference sequences of order . Mathematica Slovaca, 63, 849–862.

Karakaya, V., Şimşek, N. (2012). On some properties of new paranormed sequence space of nonabsolute type. Abstract and Applied Analysis, 2012, 921613.

Kirişçi, M., Başar, F. (2010). Some new sequence spaces derived by the domain of generalized difference matrix. Computers & Mathematics with Applications, 60, 1299-1309.

Lascarides, C.G., Maddox, I.J. (1970). Matrix transformations between some classes of sequences. Mathematical Proceedings of the Cambridge Philosophical Society, 68, 99-104.

Maddox, I.J. (1967). Spaces of strongly summable sequences. The Quarterly Journal of Mathematics, 18 (2), 345–355.

Maddox, I.J. (1968). Paranormed sequence spaces generated by infinite matrices. Mathematical Proceedings of the Cambridge Philosophical Society, 64, 335–340.

Maddox, I.J. (1988). Elements of Functional Analysis. The University Press, Cambridge.

Malkowsky, E. (1997). Recent results in the theory of matrix transformations in sequence spaces. Matematički Vesnik, 49, 187–196.

Malkowsky, E., Özger, F., Velickovic, V. (2017). Some mixed paranorm spaces. Filomat, 31, 1079–1098.

Malkowsky, E., Özger, F., Velickovic, V. (2017). Matrix transformations on mixed paranorm spaces. Filomat, 31, 2957–2966.

Malkowsky, E., Savas, E. (2004). Matrix tansformations between sequence spaces of generalized weighted mean. Applied Mathematics and Computation, 147, 333-345.

Nakano, H. (1951). Modulared sequence spaces, Proceedings of the Japan Academy, Series A, Mathematical Sciences, 27 (2), 508-512.

Simons, S. (1965). The sequence spaces and . Proceedings of the London Mathematica Society, 15 (3), 422–436.

Yaying, T. (2022). Paranormed Riesz difference sequence spaces of fractional order. Kragujevac Journal of Mathematics, 46 (2), 175–191.

Downloads

Published

2023-12-26

How to Cite

Karakaş, M., & Dağlı, M. C. (2023). A New Paranormed Sequence Space Defined by Regular Bell Matrix. Dera Natung Government College Research Journal, 8(1), 30–45. https://doi.org/10.56405/dngcrj.2023.08.01.03

Issue

Section

Articles