Research Article
Year 2024,
Issue: 46, 40 - 50, 29.03.2024
Abstract
References
- J.-P. Allouche, T. Johnson, Narayana's cows and delayed morphisms, Journées d'Informatique Musicale (1996) 6 pages.
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- C. Flaut, V. Shpakivskyi, On generalized Fibonacci quaternions and Fibonacci-Narayana quaternions, Advances in Applied Clifford Algebras 23 (3) (2013) 673-688.
- T. Goy, On identities with multinomial coefficients for Fibonacci-Narayana sequence, Annales Mathematicae et Informaticae 49 (2018) 75-84.
- J. L. Ramírez, V. F. Sirvent, A note on the k-Narayana sequence, Annales Mathematicae et Informatica 45 (2015) 91-105.
- R. Zatorsky, T. Goy, Parapermanents of triangular matrices and some general theorems on number sequences, Journal of Integer Sequences 19 (2) (2016) Article 16.2.2 23 pages.
- Y. Soykan, On generalized Narayana numbers, International Journal of Advances in Applied Mathematics and Mechanics 7 (3) (2020) 43-56.
- P.-N. Ng, P.-Y. Lee, Cesáro sequences spaces of non-absolute type, Commentationes Mathematicae (Prace Matematyczne) 20 (2) (1978) 429-433.
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- B. Altay, F. Başar, M. Mursaleen, On the Euler sequence spaces which include the spaces $\ell_p$ and $\ell_\infty$, Information Sciences 176 (10) (2006) 1450-1462.
- M. Şengonül, F. Başar, Some new Cesáro sequence spaces of non-absolute type which include, Soochow Journal of Mathematics 31 (1) (2005) 107-119.
- M. Kirişçi, F. Başar, Some new sequence spaces derived by the domain of generalized difference matrix, Computers & Mathematics with Applications 60 (5) (2010) 1299-1309.
- S. Erdem, S. Demiriz, A study on strongly almost convergent and strongly almost null binomial double sequence spaces, Fundamental Journal of Mathematics and Applications 4 (4) (2021) 271-279.
- F. Başar, Summability theory and its applications, 2nd Edition, Chapman and Hall/CRC, New York, 2022.
- J. Boos, F. P. Cass, Classical and modern methods in summability, Oxford University Press, Oxford, 2000.
- E. E. Kara, Some topological and geometrical properties of new Banach sequence spaces, Journal of Inequalities and Applications 2013 (1) (2013) Article Number 38 15 pages.
- M. Candan, E. E. Kara, A study of topological and geometrical characteristics of new Banach sequence spaces, Gulf Journal of Mathematics 3 (4) (2015) 67-84.
- E. E. Kara, M. Ilkhan, Some properties of generalized Fibonacci sequence spaces, Linear and Multilinear algebra 64 (11) (2016) 2208-2223.
- M. Karakaş, A. M. Karakaş, New Banach sequence spaces that is defined by the aid of Lucas numbers, Iğdır University Journal of the Institute of Science and Technology 7 (4) (2017) 103-111.
- M. Karakaş, A. M. Karakaş, A study on Lucas difference sequence spaces $\ell_p(\hat{E}(r, s))$ and $\ell_\infty(\hat{E}(r, s))$, Maejo International Journal of Science and Technology 12 (1) (2018) 70-78.
- T. Yaying, B. Hazarika, S. A. Mohiuddine, On difference sequence spaces of fractional-order involving Padovan numbers, Asian-European Journal of Mathematics 14 (06) (2021) 2150095 22 pages.
- M. İ. Kara, E. E. Kara, Matrix transformations and compact operators on Catalan sequence spaces, Journal of Mathematical Analysis and Applications 498 (1) (2021) 124925 17 pages.
- M. Karakaş, On the sequence spaces involving Bell numbers, Linear and Multilinear Algebra 71 (14) (2023) 2298-2309.
- M. C. Dağli, A new almost convergent sequence space defined by Schröder matrix, Linear and Multilinear Algebra 71 (11) (2023) 1863-1874.
- A. Wilansky, Summability through functional analysis, Elsevier, Amsterdam, 2000.
- A. M. Jarrah, E. Malkowsky, Ordinary, absolute and strong summability and matrix transformations, Filomat 17 (2003) 59-78.
- M. Stieglitz, H. Tietz, Matrix transformationen von Folgenräumen Eine Ergebnisübersicht, Mathematische Zeitschrift 154 (1977) 1-16.
Year 2024,
Issue: 46, 40 - 50, 29.03.2024
Abstract
In this paper, we first establish the regular matrix $N$ using Narayana numbers. Then, we create new normed sequence spaces $Z(N)$ using the matrix $ N$ and demonstrate that these spaces are linearly isomorphic to $Z$ where $Z\in\{c_0, c, \ell_p, \ell_\infty\}$. Additionally, we provide inclusion relations for the spaces $c_0(N)$, $c(N)$, $\ell_p(N)$, and $\ell_\infty(N)$. Furthermore, we construct the Schauder bases of the $c_0(N)$, $c(N)$, and $\ell_p(N)$. Finally, we compute the $\alpha$-, $\beta$-, and $\gamma$-duals of these spaces and characterize the classes $(Z(N),X)$ for the certain choice of the sequence space $X$.
References
- J.-P. Allouche, T. Johnson, Narayana's cows and delayed morphisms, Journées d'Informatique Musicale (1996) 6 pages.
- A. N. Singh, On the use of series in Hindu mathematics, Osiris 1 (1936) 606-628.
- T. Koshy, Fibonacci and Lucas numbers with applications, 2nd Edition, John Wiley & Sons, New Jersey, 2019.
- N. Sloane, The on-line encyclopedia of integer sequences, Mathematicae et Informaticae 41 (2013) 219-234.
- G. Bilgici, The generalized order-$k$ Narayana's cows numbers, Mathematica Slovaca 66 (4) (2016) 795-802.
- T. V. Didkivska, M. St'opochkina, Properties of Fibonacci-Narayana numbers, In the World of Mathematics 9 (1) (2003) 29-36.
- C. Flaut, V. Shpakivskyi, On generalized Fibonacci quaternions and Fibonacci-Narayana quaternions, Advances in Applied Clifford Algebras 23 (3) (2013) 673-688.
- T. Goy, On identities with multinomial coefficients for Fibonacci-Narayana sequence, Annales Mathematicae et Informaticae 49 (2018) 75-84.
- J. L. Ramírez, V. F. Sirvent, A note on the k-Narayana sequence, Annales Mathematicae et Informatica 45 (2015) 91-105.
- R. Zatorsky, T. Goy, Parapermanents of triangular matrices and some general theorems on number sequences, Journal of Integer Sequences 19 (2) (2016) Article 16.2.2 23 pages.
- Y. Soykan, On generalized Narayana numbers, International Journal of Advances in Applied Mathematics and Mechanics 7 (3) (2020) 43-56.
- P.-N. Ng, P.-Y. Lee, Cesáro sequences spaces of non-absolute type, Commentationes Mathematicae (Prace Matematyczne) 20 (2) (1978) 429-433.
- C.-S. Wang, On Nörlund sequence spaces, Tamkang Journal of Mathematics 9 (1) (1978) 269-274.
- B. Altay, F. Başar, M. Mursaleen, On the Euler sequence spaces which include the spaces $\ell_p$ and $\ell_\infty$, Information Sciences 176 (10) (2006) 1450-1462.
- M. Şengonül, F. Başar, Some new Cesáro sequence spaces of non-absolute type which include, Soochow Journal of Mathematics 31 (1) (2005) 107-119.
- M. Kirişçi, F. Başar, Some new sequence spaces derived by the domain of generalized difference matrix, Computers & Mathematics with Applications 60 (5) (2010) 1299-1309.
- S. Erdem, S. Demiriz, A study on strongly almost convergent and strongly almost null binomial double sequence spaces, Fundamental Journal of Mathematics and Applications 4 (4) (2021) 271-279.
- F. Başar, Summability theory and its applications, 2nd Edition, Chapman and Hall/CRC, New York, 2022.
- J. Boos, F. P. Cass, Classical and modern methods in summability, Oxford University Press, Oxford, 2000.
- E. E. Kara, Some topological and geometrical properties of new Banach sequence spaces, Journal of Inequalities and Applications 2013 (1) (2013) Article Number 38 15 pages.
- M. Candan, E. E. Kara, A study of topological and geometrical characteristics of new Banach sequence spaces, Gulf Journal of Mathematics 3 (4) (2015) 67-84.
- E. E. Kara, M. Ilkhan, Some properties of generalized Fibonacci sequence spaces, Linear and Multilinear algebra 64 (11) (2016) 2208-2223.
- M. Karakaş, A. M. Karakaş, New Banach sequence spaces that is defined by the aid of Lucas numbers, Iğdır University Journal of the Institute of Science and Technology 7 (4) (2017) 103-111.
- M. Karakaş, A. M. Karakaş, A study on Lucas difference sequence spaces $\ell_p(\hat{E}(r, s))$ and $\ell_\infty(\hat{E}(r, s))$, Maejo International Journal of Science and Technology 12 (1) (2018) 70-78.
- T. Yaying, B. Hazarika, S. A. Mohiuddine, On difference sequence spaces of fractional-order involving Padovan numbers, Asian-European Journal of Mathematics 14 (06) (2021) 2150095 22 pages.
- M. İ. Kara, E. E. Kara, Matrix transformations and compact operators on Catalan sequence spaces, Journal of Mathematical Analysis and Applications 498 (1) (2021) 124925 17 pages.
- M. Karakaş, On the sequence spaces involving Bell numbers, Linear and Multilinear Algebra 71 (14) (2023) 2298-2309.
- M. C. Dağli, A new almost convergent sequence space defined by Schröder matrix, Linear and Multilinear Algebra 71 (11) (2023) 1863-1874.
- A. Wilansky, Summability through functional analysis, Elsevier, Amsterdam, 2000.
- A. M. Jarrah, E. Malkowsky, Ordinary, absolute and strong summability and matrix transformations, Filomat 17 (2003) 59-78.
- M. Stieglitz, H. Tietz, Matrix transformationen von Folgenräumen Eine Ergebnisübersicht, Mathematische Zeitschrift 154 (1977) 1-16.
There are 31 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Operator Algebras and Functional Analysis |
| Journal Section | Research Article |
| Authors | |
| Early Pub Date | March 28, 2024 |
| Publication Date | March 29, 2024 |
| Submission Date | December 20, 2023 |
| Acceptance Date | February 29, 2024 |
| Published in Issue | Year 2024 Issue: 46 |
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