Research Article
Year 2025,
Volume: 38 Issue: 2, 865 - 872, 01.06.2025
Abstract
References
- [1] Banaś, J. and Krajewska, M., “Existence of solutions for infinite systems of differential equations in spaces of tempered sequences”, Electronic Journal of Differential Equantios, 2017(60): 1-28, (2017).
- [2] Haque, I., Ali, J., and Mursaleen, M., “Solvability of an infinite system of Langevin fractional differential equations in a new tempered sequence space”, Fractional Calculus and Applied Analysis, 26: 1894-1915, (2023). DOI: https://doi.org/10.1007/s13540-023-00175-y
- [3] Das, A., Mohiuddine, S.A., Alotaibi, A., and Deuri, B. C., “Generalization of Darbo-type theorem and application on existence of implicit fractional integral equations in tempered sequence spaces”, Alexandria Engineering Journal, 61(3): 2010-2015, (2022). DOI: https://doi.org/10.1016/j.aej.2021.07.031
- [4] Haque, I., Ali, J., and Mursaleen, M., “Existence of solutions for an infinite systems of Hilfer fractional boundary value problems in tempered sequence spaces”, Alexandria Engineering Journal, 65: 575-583, (2023). DOI: https://doi.org/10.1016/j.aej.2022.09.032
- [5] Mohiuddine, S.A., Das, A., and Alotaibi, A., “Existence of solutions for nonlinear integral equations in tempered sequence spaces via generalized Darbo-type theorem”, Journal of Function Spaces, 2022, Article ID 4527439, 1-8, (2022). DOI: https://doi.org/10.1155/2022/4527439
- [6] Mursaleen, M., and Başar, F., Sequence Spaces: Topics in Modern Summability Theory, CRC Press, Boca Raton, (2020).
- [7] Salem, A., Almaghamsi, L., and Alzahrani, F., “An infinite system of fractional order with p-Laplacian operator in a tempered sequence space via measure of noncompactness technique”, Fractal Fractional, 5(4): Article 182, (2021). DOI: https://doi.org/10.3390/fractalfract5040182
- [8] Rabbani, M., Das, A., Hazarika, B., and Arab, R., “Measure of noncompactness of a new space of tempered sequences and its application on fractional differential equations”, Chaos, Solitons & Fractals, 140: 1-7, (2020). DOI: https://doi.org/10.1016/j.chaos.2020.110221
- [9] Grossman, M. and Katz, R., Non-Newtonian Calculus, Lee Press, Masschusetts, (1872).
- [10] Bashirov, A.E., Kurpınar, E. M. and Özyapıcı, A., “Multiplicative calculus and its applications”, Journal of Mathematical Analysis and Applications, 337(1): 36-48, (2008). DOI: https://doi.org/10.1016/j.jmaa.2007.03.081
- [11] Binbaşıoğlu, D., Demiriz, S. and Türkoğlu, D., “Fixed points of non-Newtonian contraction mappings on non-Newtonian metric spaces”, Journal of Fixed Point Theory and Applications, 18: 213-224, (2016). DOI: https://doi.org/10.1007/s11784-015-0271-y
- [12] Binbaşıoğlu, D., “On fixed point results for generalized contractıons in non-Newtonian metric spaces”, Cumhuriyet Science Journal, 43(2), 289-293, (2022). DOI: https://doi.org/10.17776/csj.1007806
- [13] Çakmak, A.F., and Başar, F., “Some new results on sequence spaces with respect to non-Newtonian calculus”, Journal of Inequalities and Applications, 2012(228): 1-17, (2012). DOI: https://doi.org/10.1186/1029-242X-2012-228
- [14] Çakmak, A.F., and Başar, F., “Certain spaces of functions over the field of non-Newtonian complex numbers”, Abstract and Applied Analysis, 2014, Article ID 236124, 1-12, (2014). DOI: https://doi.org/10.1155/2014/236124
- [15] Güngör, N., “Some geometric properties of the non-Newtonian sequence l_p (N)”, Mathematica Slovaca, 70(3): 689-696, (2020). DOI: https://doi.org/10.1515/ms-2017-0382
- [16] Rohman, M., and Eryılmaz, İ., “Some basic results in ν-normed spaces”, Indonesian Journal of Mathematics and Applications, 1(1): 1-8, (2023). DOI: https://doi.org/10.21776/ub.ijma.2023.001.01.1
Year 2025,
Volume: 38 Issue: 2, 865 - 872, 01.06.2025
Abstract
In this paper, we will introduce tempered ν-sequence spaces generated by directed preserving generator ν. After building the spaces, we investigate and show tempered ν-sequence spaces are Banach spaces. In addition, we also find that there is an isomorphism between tempered ν-sequence spaces and the classical one. The direct implication is that some tempered ν-sequence spaces have a Schauder basis.
References
- [1] Banaś, J. and Krajewska, M., “Existence of solutions for infinite systems of differential equations in spaces of tempered sequences”, Electronic Journal of Differential Equantios, 2017(60): 1-28, (2017).
- [2] Haque, I., Ali, J., and Mursaleen, M., “Solvability of an infinite system of Langevin fractional differential equations in a new tempered sequence space”, Fractional Calculus and Applied Analysis, 26: 1894-1915, (2023). DOI: https://doi.org/10.1007/s13540-023-00175-y
- [3] Das, A., Mohiuddine, S.A., Alotaibi, A., and Deuri, B. C., “Generalization of Darbo-type theorem and application on existence of implicit fractional integral equations in tempered sequence spaces”, Alexandria Engineering Journal, 61(3): 2010-2015, (2022). DOI: https://doi.org/10.1016/j.aej.2021.07.031
- [4] Haque, I., Ali, J., and Mursaleen, M., “Existence of solutions for an infinite systems of Hilfer fractional boundary value problems in tempered sequence spaces”, Alexandria Engineering Journal, 65: 575-583, (2023). DOI: https://doi.org/10.1016/j.aej.2022.09.032
- [5] Mohiuddine, S.A., Das, A., and Alotaibi, A., “Existence of solutions for nonlinear integral equations in tempered sequence spaces via generalized Darbo-type theorem”, Journal of Function Spaces, 2022, Article ID 4527439, 1-8, (2022). DOI: https://doi.org/10.1155/2022/4527439
- [6] Mursaleen, M., and Başar, F., Sequence Spaces: Topics in Modern Summability Theory, CRC Press, Boca Raton, (2020).
- [7] Salem, A., Almaghamsi, L., and Alzahrani, F., “An infinite system of fractional order with p-Laplacian operator in a tempered sequence space via measure of noncompactness technique”, Fractal Fractional, 5(4): Article 182, (2021). DOI: https://doi.org/10.3390/fractalfract5040182
- [8] Rabbani, M., Das, A., Hazarika, B., and Arab, R., “Measure of noncompactness of a new space of tempered sequences and its application on fractional differential equations”, Chaos, Solitons & Fractals, 140: 1-7, (2020). DOI: https://doi.org/10.1016/j.chaos.2020.110221
- [9] Grossman, M. and Katz, R., Non-Newtonian Calculus, Lee Press, Masschusetts, (1872).
- [10] Bashirov, A.E., Kurpınar, E. M. and Özyapıcı, A., “Multiplicative calculus and its applications”, Journal of Mathematical Analysis and Applications, 337(1): 36-48, (2008). DOI: https://doi.org/10.1016/j.jmaa.2007.03.081
- [11] Binbaşıoğlu, D., Demiriz, S. and Türkoğlu, D., “Fixed points of non-Newtonian contraction mappings on non-Newtonian metric spaces”, Journal of Fixed Point Theory and Applications, 18: 213-224, (2016). DOI: https://doi.org/10.1007/s11784-015-0271-y
- [12] Binbaşıoğlu, D., “On fixed point results for generalized contractıons in non-Newtonian metric spaces”, Cumhuriyet Science Journal, 43(2), 289-293, (2022). DOI: https://doi.org/10.17776/csj.1007806
- [13] Çakmak, A.F., and Başar, F., “Some new results on sequence spaces with respect to non-Newtonian calculus”, Journal of Inequalities and Applications, 2012(228): 1-17, (2012). DOI: https://doi.org/10.1186/1029-242X-2012-228
- [14] Çakmak, A.F., and Başar, F., “Certain spaces of functions over the field of non-Newtonian complex numbers”, Abstract and Applied Analysis, 2014, Article ID 236124, 1-12, (2014). DOI: https://doi.org/10.1155/2014/236124
- [15] Güngör, N., “Some geometric properties of the non-Newtonian sequence l_p (N)”, Mathematica Slovaca, 70(3): 689-696, (2020). DOI: https://doi.org/10.1515/ms-2017-0382
- [16] Rohman, M., and Eryılmaz, İ., “Some basic results in ν-normed spaces”, Indonesian Journal of Mathematics and Applications, 1(1): 1-8, (2023). DOI: https://doi.org/10.21776/ub.ijma.2023.001.01.1
There are 16 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Operator Algebras and Functional Analysis |
| Journal Section | Mathematics |
| Authors | |
| Early Pub Date | March 8, 2025 |
| Publication Date | June 1, 2025 |
| Submission Date | December 13, 2023 |
| Acceptance Date | February 15, 2025 |
| Published in Issue | Year 2025 Volume: 38 Issue: 2 |