On Λ-Fibonacci difference sequence spaces of fractional order
DOI:
https://doi.org/10.56405/dngcrj.2021.06.01.10Keywords:
Fibonacci sequence, Difference operator, Lambda sequence, Lambda-Fibonacci difference sequence spaces, Schauder basisAbstract
In this article, we introduce -Fibonacci difference operator of fractional order which is obtained by the composition of -Fibonacci matrix and backward fractional difference operator defined by and introduce the sequence spaces and We give some topological properties, and obtain the Schauder basis of the new spaces.
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Alotaibi, A., Mursaleen, M., Alamri, B., Mohiuddine, S.A. (2015). Compact operators on some Fibonacci difference sequence spaces. Journal of Inequalities and Applications, 2015, 2013.
Baliarsingh, P., Dutta, S. (2015a). A unifying approach to the difference operators and their applications. Boletim Sociedade Paranaense de Matemática, 33 (2015), 49-57.
Baliarsingh, P., Dutta, S. (2015b). On the classes of fractional order difference sequence spaces and their matrix transformations. Applied Mathematics and Computation, 250 (2015), 665-674.
Baliarsingh, P. (2013). Some new difference sequence spaces of fractional order and their dual spaces. Applied Mathematics and Computation, 219 (2013), 9737-9742.
Başarır, M., Başar, F., Kara, E.E. (2016). On the spaces of Fibonacci difference absolutely p-summable, null and convergent sequences. Sarajevo Journal of Mathematics, 12 (25), 167-182.
Bektas, C., Et, M., Ҫolak, R. (2004). Generalized difference sequence spaces and their dual spaces. Journal of Mathematical Analysis Application, 292 (2004), 423-432.
Candan, M. (2015). A new approach on the spaces of generalized Fibonacci difference null and convergent sequences. Math. Aeterna, 5 (1) (2015), 191-210.
Das, A., Hazarika, B. (2017). Some new Fibonacci difference spaces of non-absolute type and compact operators. Linear and Multilinear Algebra, 65 (12) (2017), 2551-2573.
Das, A., Hazarika, B., Kara, E.E., Başar, F. (2022), On composition operators of Fibonacci matrix and applications of Hausdorff measure of noncompactness. Boletim de Sociedade Paranaense, doi: https://doi.org/10.5269/bspm.39960
Et, M., Ҫolak, R. (1995). On generalized difference sequence spaces. Soochow Journal of Mathematics, 21, 377-386.
Et, M., Esi, M. (2000). On Köthe-Toeplitz duals of generalized difference sequence spaces. Bulletin of Malaysian Mathematical Science Soiety, 231 (2000), 25-32.
Et, M., Başarır, M. (1997). On some new generalized difference sequence spaces. Periodica Mathematica Hungarica, 35 (1997), 169-175.
Kara, E.E. (2013). Some topological and geometric properties of new Banach sequence spaces. Journal of Inequalities and Applications, 2013, 38.
Kara, E.E., Demiriz, S. (2015). Some new paranormed difference sequence spaces derived by Fibonacci numbers. Miskolc Mathematical Notes, 16 (2015), 907-923.
Kızmaz, H. (1981). On certain sequence spaces. Canadian Mathematical Bulletin, 24, 169-176.
Koshy, T. (2021). Fibonacci and Lucus numbers with applications. Wiley, New York.
Malkowsky, E., Parashar, S.D. (1997). Matrix transformations in spaces of bounded and convergent difference sequences of order m. Analysis, 17 (1997), 87-97.
Mursaleen, M., Noman, A.K. (2010a). On the spaces of λ-convergent and bounded sequences. Thai Journal of Mathematics, 8 (2010), 311-329.
Mursaleen, M., Noman, A.K. (2010b). On some new difference sequence spaces of non-absolute type, Mathematical and Computer modelling. 52 (2010), 603-617.
Wilansky, A. (1984). Summability through Functional Analysis. North-Holland Mathematics Studies, 85. Elsevier, Amsterdam.
Yaying, T. (2019). On a new class of generalized difference sequence spaces of fractional order defined by modulus function. Proyecciones, 38 (3), 485-497.
Yaying, T. (2021). On the paranormed Nörlund difference sequence space of fractional order and geometric
properties. Mathematica Slovaca, 71 (1), 155-170.
Yaying, T., Hazarika, B., Mohiuddine, S.A. (2021a). On difference sequence spaces of fractional-order involving Padovan numbers. Asian-European Journal of Mathematics, 14 (6), 2150095.
Yaying, T., Hazarika, B., Et, M. (2021b). Matrix mappings and Hausdorff measure of non-compactness on Riesz difference spaces of fractional order. The Journal of Analysis, 29, 1443-1460.
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