A new band matrix with q-Fibonacci
DOI:
https://doi.org/10.56405/dngcrj.2025.10.01.03Keywords:
q-Fibonacci Numbers; q-Fibonacci analogue; Dual spaces; Matris Transformation.Abstract
In this research paper, we define the Schröder basis of the space defined by a new q-Fibonacci band matrix. We determine its dual spaces and matrix transformations. Finally, we prove that this space is of Banach-Saks type p and has the weak fixed point property.
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Aktuğlu, H., & Bekar, Ş. (2011). On q-Cesàro matrix and q-statistical convergence. Journal of Computational and Applied Mathematics, 235 (16), 4717-4723.
Andrews, G.E. (2004). Fibonacci numbers and the Rogers-Ramanujan identities. Fibonacci Quarterly, 42 (1), 3-19.
Atabey, K. İ., Çınar, M., & Et, M. (2023). q-Fibonacci sequence spaces and related matrix transformations. Journal of Applied Mathematics and Computing, 69, 2135–2154.
Atabey, K. İ., Çınar, M., & Et, M. (2025a). New Triangular q-Fibonacci Matrix. Filomat, 39 (2), 601–615.
Atabey, K. İ., Çınar, M., & Et, M. (2025b). q-Fibonacci statistical convergence. Georgian Mathematical Journal, 32 (5), 759-766.
Atabey, K. İ. (2025). On Sequence Spaces of New q-Fibonacci Band Matrix. In M. F. Karaaslan (Ed.), Proceedings of International Conference on Mathematics and Computers with Applications, (pp. 206–215) ISBN 978-625-96744-0-7.
Aytaç, P. (2018). Some Arithmetic Properties of q-Fibonacci Numbers. Master thesis, Akdeniz University.
Başar, F. & Dutta H. (2020). Summable spaces and their duals, matrix transformations and geometric properties. CRC Press, https://doi.org/10.1201/9781351166928
Carlitz, L. (1974). Fibonacci Notes-3: q-Fibonacci Numbers. Fibonacci Quarterly, 12 (4), 317–322. https://doi.org/10.1080/00150517.1974.12430696.
Çınar, M., & Et, M. (2020). q-Double Cesàro Matrices and q-Statistical Convergence of Double Sequences. National Academy Science Letters, 43 (1), 73-76.
Dağlı, M. (2023). A novel conservative matrix arising from Schröder numbers and its properties, Linear and Multilinear Algebra, 71 (8), 1338-1351.
Demiriz, S., & Şahin, A. (2016). q-Cesàro sequence spaces derived by q-analogues, Advances in Mathematics, 5 (2), 97-110.
Diestel, J. (2012). Sequences and series in Banach spaces (Vol. 92). Springer Science and Business Media, 2012.
Ellidokuzoglu, H. B., Demiriz, S. & Kara, M.İ. (2025). q-Schroder sequence spaces and Schroder core. Filomat, 39 (2), 715-729.
García-Falset, J. (1994). Stability and fixed points for nonexpansive mappings. Houston Journal of Mathematics, 20(3), 495-506.
García-Falset, J. (1997). The fixed point property in Banach spaces with the NUS-property. Journal of Mathematical Analysis and Applications, 215 (2), 532-542.
Hudzik, H., Karakaya, V., Mursaleen, M. & Şimsek, N. (2014). Banach-Saks type and Gurariǐ modulus of convexity of some Banach sequence spaces. Abstract and Applied Analysis, 2014, 427382, 9 pages.
Hirschhor, M. D. (1972). Partitions and Ramanujan’s continued fraction. Duke Mathematical Journal, 39 (4), 789-791.
Mursaleen, M., Başar, F., & Altay, B. (2006). On the Euler sequence spaces which include the spaces l_p and l_∞. Nonlinear Analysis: Theory, Methods and Applications, 65 (3), 707-717.
Kac, V., & Cheung, P. (2002). Quantum Calculus. Springer, New York.
Kananthai, A., Mursaleen, M., Sanhan, W., & Suantai, S. (2002). On property (H) and rotundity of difference sequence spaces. Journal of Nonlinear and Convex analysis, 3 (3), 401-410.
Kara, E. E. (2013). Some topological and geometrical properties of new Banach sequence spaces. Journal of Inequalities and Applications, 2013 (1), 1-15.
Kirişçi, M., & Başar, F. (2010). Some new sequence spaces derived by the domain of generalized difference matrix. Computers and Mathematics with Applications, 60 (5), 1299-1309.
Koshy, T. (2001). Fibonacci and Lucas numbers with applications. John Wiley and Sons.
Knaust, H. (1992). Orlicz sequence spaces of Banach-Saks type. Archiv der Mathematik, 59 (6), 562-565.
Schur, I. (1917). Ein Beitrag zur Additiven Zahlentheorie, Sitzungsber. Akad. Wissensch. Berlin, Phys. Math. Klasse, 302-321.
Savaş, E., Karakaya, V., & Şimşek, N. (2009). Some l_p-type new sequence spaces and their geometric properties. Abstract and Applied Analysis, 2009, 696971.
Selmanoğulları, T., Savaş, E., & Rhoades, B.E. (2011). On q-Hausdorff matrices. Taiwanese Journal of Mathematics, 15 (6), 2429-2437.
Stieglitz, M., & Tietz, H. (1977). Matrixtransformationen von Folgenräumen Eine Ergebnisübersicht. (German) Mathematische Zeitschrift, 154 (1), 1-16
Yaying, T., Hazarika, B., & Mursaleen, M. (2021). On sequence space derived by the domain of q-Cesàro matrix in l_p space and the associated operator ideal. Journal of Mathematical Analysis and Application, 493 (1), 1-17.
Yaying, T., Hazarika, B., & Et, M. (2023). On some sequence spaces via q-Pascal matrix and its geometric properties. Symmetry, 15(9), 1659.
Yaying, T., Hazarika, B., Tripathy, B. C., & Mursaleen, M. (2022). The Spectrum of Second Order Quantum Difference Operator. Symmetry, 14(3), 557.
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