Fractional ordered Euler Riesz difference sequence spaces
DOI:
https://doi.org/10.22199/issn.0717-6279-5663Keywords:
Euler-Riesz difference sequence space, difference operator (∆τ), Schauder basis, Euler-Riesz difference sequence space, difference operator (∆τ ), Schauder basis, infinite matrices and α−, β− and γ−duals, β− and γ−dualsAbstract
In this article we introduce new sequence spaces c0 (τ), c(τ) and l∞(τ) of fractional order τ , consisting of an operator which is a composition of Euler-Riesz operator and fractional difference operator. Certain topological properties of these spaces are investigated along with Schauder basis and α−, β− and γ−duals.
References
A. Sönmez and F. Başar, ”Generalized Difference Spaces of Non-Absolute Type of Convergent and Null Sequences”, Abstract and Applied Analysis, Article ID 435076, p. 20, 2012. https://doi.org/10.1155/2012/435076
B. Altay and F. Başar, ”On some Euler sequence spaces of nonabsolute type”, Ukrainian Mathematical Journal, vol. 57, 1-17, 2005. https://doi.org/10.1007/s11253-005-0168-9
B. Altay and F. Başar, ”On the paranormed Riesz sequence space of non-absolute type”, Southeast Asian Bulletin of Mathematics, vol. 26, pp. 701-715, 2002.
B. Altay and F. Başar, ”Some paranormed Riesz sequence spaces of non-absolute type”, Southeast Asian Bulletin of Mathematics, vol. 30, pp. 591-608, 2006.
B. Altay, F. Başar and M. Mursaleen, ”On the Euler sequence spaces which include the spaces lp and l∞, I”, Information Sciences, vol. 176, pp. 1450-1462, 2006. https://doi.org/10.1016/j.ins.2005.05.008
B. Altay and H. Polat, ”On some new Euler difference sequence spaces”, Southeast Asian Bulletin of Mathematics, vol. 30, pp. 209-220, 2006.
E. Malkowsky, ”Recent results in the theory of matrix transformations in sequence spaces”, Matematički Vesnik, vol. 49, pp. 187-196, 1997.
F. Başar and N. L. Braha, ”Euler- Cesaro Difference Spaces of Bounded, Convergent and Null Sequences” Tamkang Journal of Mathematics, vol. 47, no. 4, pp. 405-420, 2016. https://doi.org/10.5556/j.tkjm.47.2016.2065
H. Kızmaz, ”On certain sequence spaces”, Canadian Mathematical Bulletin, vol. 24, pp. 169-176, 1981.https://doi.org/10.4153/CMB-1981-027-5
H. Polat and F. Başar, ”Some Euler spaces of difference sequences of order m”, Acta Mathematica Scientia, vol. 27, no. 2, pp. 254-266, 2007. https://doi.org/10.1016/S0252-9602(07)60024-1
I. J. Maddox, Elements of Functional Analysis, 2nd ed., Cambridge University Press, Cambridge, 1988.
I. J. Maddox, ”Paranormed sequence spaces generated by infinite matrices”, Mathematical Proceedings of the Cambridge Philosophical Society, vol. 64, pp. 335-340, 1968. https://doi.org/10.1017/S0305004100042894
I. J. Maddox, ”Spaces of strongly summable sequences”, The Quarterly Journal of Mathematics, vol. 18, pp. 345-355, 1967. https://doi.org/10.1093/qmath/18.1.345
K. G. Grosse-Erdmann, ”Matrix transformation between the sequence spaces of Maddox”, Journal of Mathematical Analysis and Applications, vol. 180, no. 1, pp. 223-238, 1993. https://doi.org/10.1006/jmaa.1993.1398
M. Basarir and M. Öztürk, ”On the Riesz difference sequence space”, Rendiconti del Circolo Matematico di Palermo, vol. 2, no. 57, pp. 377-389, 2008. https://doi.org/10.1007/s12215-008-0027-2
M. Et and M. Basarir, ”On some new generalized difference sequence spaces”, Periodica Mathematica Hungarica, vol. 35, pp. 169-175, 1997. https://doi.org/10.1023/A:1004597132128
M. Et and R. Çolak, ”On generalized difference sequence spaces”, Soochow Journal of Mathematics, vol. 21, pp. 377-386, 1995.
M. Mursaleen and K. Noman, ”On Some new sequence spaces of non-absolute type related to the spaces lp and l∞- I”, Filomat, vol. 25, no. 2, pp. 33-51, 2011. https://doi.org/10.2298/FIL1102033M
M. Mursaleen and K. Noman, ”On Some new sequence spaces of non-absolute type related to the spaces lp and l∞- II”, Mathematical Communications, vol. 16, pp. 383-398, 2011.
M. Mursaleen, ”Generalized spaces of difference sequences”, Journal of Mathematical Analysis and Applications, vol. 203, pp. 738-745, 1996. https://doi.org/10.1006/jmaa.1996.0409
P. Baliarsingh and S. Dutta, ”A unifying approach to the difference operators and their applications”, Boletim da Sociedade Paranaense de Matemática, vol. 33, pp. 49-57, 2015.
P. Baliarsingh and S. Dutta, ”On the classes of fractional order difference sequence spaces and their matrix transformations”, Applied Mathematics and Computation, vol. 250, pp. 665-674, 2015. https://doi.org/10.1016/j.amc.2014.10.121
P. Baliarsingh and S. Dutta, ”On an explicit formula for inverse of triangular matrices”, Journal of the Egyptian Mathematical Society, vol. 23, pp. 297-302, 2015.
P. Baliarsingh, ”Some new difference sequence spaces of fractional order and their dual spaces”, Applied Mathematics and Computation, vol. 219, pp. 9737-9742, 2013. https://doi.org/10.1016/j.amc.2013.03.073
S. Dutta and P. Baliarsingh, ”A note on paranormed difference sequence spaces of fractional order and their matrix transformations”, Journal of the Egyptian Mathematical Society, vol. 22, pp. 249-253, 2014. https://doi.org/10.1016/j.joems.2013.07.001
S. Dutta and P. Baliarsingh, ”On some Toeplitz matrices and their inversion”, Journal of the Egyptian Mathematical Society, vol. 22, pp. 420-423, 2014. https://doi.org/10.1016/j.joems.2013.10.001
S. Simons, The sequence spaces c(pv) and m(pv), Proceedings of the London Mathematical Society, vol. 15, no. 3, pp. 422-436, 1965.
T. Yaying, ”Paranormed Riesz difference sequence spaces of fractional order”, Kragujevac Journal of Mathematics, vol. 46, pp. 175-191, 2022.
U. Kadak and P. Baliarsingh, ”On certain Euler difference sequence spaces of fractional order and related dual properties”, Journal of Nonlinear Sciences and Applications, vol. 8, pp. 997-1004, 2015. https://doi.org/10.22436/jnsa.008.06.10
Published
How to Cite
Issue
Section
Copyright (c) 2023 Diptimayee Jena, Salila Dutta
This work is licensed under a Creative Commons Attribution 4.0 International License.
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
