Abstract
The primary objective of this paper is to create a novel infinite Toeplitz matrix by leveraging Tetranacci numbers. This matrix serves as the foundation for defining new sequence spaces denoted as
Acknowledgements
We thank the editor and referees for valuable comments and suggestions for improving the paper.
References
[1] A. Aghajani, M. Mursaleen and A. Shole Haghighi, Fixed point theorems for Meir–Keeler condensing operators via measure of noncompactness, Acta Math. Sci. Ser. B (Engl. Ed.) 35 (2015), no. 3, 552–566. 10.1016/S0252-9602(15)30003-5Search in Google Scholar
[2]
A. Aghajani and E. Pourhadi,
Application of measure of noncompactness to
[3] R. R. Akhmerov, M. I. Kamenskiĭ, A. S. Potapov, A. E. Rodkina and B. N. Sadovskiĭ, Measures of Noncompactness and Condensing Operators, Oper. Theory Adv. Appl. 55, Birkhäuser, Basel, 1992. 10.1007/978-3-0348-5727-7Search in Google Scholar
[4]
A. Alotaibi, M. Mursaleen and B. A. S. Alamri,
Solvability of second order linear differential equations in the sequence space
[5] A. Alotaibi, M. Mursaleen, B. A. S. Alamri and S. A. Mohiuddine, Compact operators on some Fibonacci difference sequence spaces, J. Inequal. Appl. 2015 (2015), Paper No. 203. 10.1186/s13660-015-0713-5Search in Google Scholar
[6] A. Alotaibi, M. Mursaleen and S. A. Mohiuddine, Application of measures of noncompactness to infinite system of linear equations in sequence spaces, Bull. Iranian Math. Soc. 41 (2015), no. 2, 519–527. Search in Google Scholar
[7]
B. Altay, F. Başar and M. Mursaleen,
On the Euler sequence spaces which include the spaces
[8] J. Banaś and K. Goebel, Measures of Noncompactness in Banach Spaces, Lecture Notes Pure Appl. Math. 60, Marcel Dekker, New York, 1980. Search in Google Scholar
[9] J. Banaś and M. Lecko, Solvability of infinite systems of differential equations in Banach sequence spaces, J. Comput. Appl. Math. 137 (2001), no. 2, 363–375. 10.1016/S0377-0427(00)00708-1Search in Google Scholar
[10] J. Banaś and M. Mursaleen, Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations, Springer, New Delhi, 2014. 10.1007/978-81-322-1886-9Search in Google Scholar
[11] F. Başar, Summability Theory and its Applications, CRC Press, Boca Raton, 2022. 10.1201/9781003294153Search in Google Scholar
[12] F. Başar and H. Roopaei, Banach spaces and inequalities associated with new generalization of Cesàro matrix, Acta Math. Sci. Ser. B (Engl. Ed.) 43 (2023), no. 4, 1518–1536. 10.1007/s10473-023-0404-0Search in Google Scholar
[13] M. Başarır, F. Başar and E. E. Kara, On the spaces of Fibonacci difference absolutely p-summable, null and convergent sequences, Sarajevo J. Math. 12(25) (2016), no. 2, 167–182. 10.5644/SJM.12.2.04Search in Google Scholar
[14] R. Bellman, Methods of Nonliner Analysis. Vol. II, Math. Sci. Eng. 61, Academic Press, New York, 1973. Search in Google Scholar
[15] M. Candan, A new approach on the spaces of generalized Fibonacci difference null and convergent sequences, Math. AEterna 5 (2015), 191–210. Search in Google Scholar
[16] P. Chandra and B. C. Tripathy, On generalised Köthe–Toeplitz duals of some sequence spaces, Indian J. Pure Appl. Math. 33 (2002), no. 8, 1301–1306. Search in Google Scholar
[17] G. Darbo, Punti uniti in trasformazioni a codominio non compatto, Rend. Semin. Mat. Univ. Padova 24 (1955), 84–92. Search in Google Scholar
[18]
A. Das and B. Hazarika,
Application of measure of noncompactness to the infinite systems of second-order differential equations in Banach sequence spaces
[19] K. Deimling, Ordinary Differential Equations in Banach Spaces, Lecture Notes in Math. 596, Springer, Berlin, 1977. 10.1007/BFb0091636Search in Google Scholar
[20] D. G. Duffy, Green’s Functions with Applications, Stud. Adv. Math., Chapman & Hall/CRC, Boca Raton, 2001. Search in Google Scholar
[21] M. Feinberg, Fibonacci-Tribonacci, Fibonacci Quart. 1.3 (1963), 71–74. 10.1080/00150517.1963.12431573Search in Google Scholar
[22] M. Karakaş, A new regular matrix defined by Fibonacci numbers and its applications, BEU J. Sci. 4 (2015), no. 2, 205–210. 10.17798/beufen.78452Search in Google Scholar
[23] V. A. Khan, I. A. Khan, SK A. Rahaman and A. Ahmad, On Tribonacci I-convergent sequence spaces, J. Math. Comput. SCI-JM. 24 (2022), no. 3, 225–234. 10.22436/jmcs.024.03.04Search in Google Scholar
[24] G. Köthe and O. Toeplitz, Lineare Räume mit unendlich vielen Koordinaten und Ringe unendlicher Matrizen, J. Reine Angew. Math. 171 (1934), 193–226. 10.1515/crll.1934.171.193Search in Google Scholar
[25] C. Kuratowski, Sur les espaces complets, Fund. Math. 15 (1930), 301–309. 10.4064/fm-15-1-301-309Search in Google Scholar
[26] W. I. McLaughlin, Note on a Tetranacci alternative to Bodefs law, Fibonacci Quart. 17 (1979), no. 2, 116–117. 10.1080/00150517.1979.12430236Search in Google Scholar
[27] A. Meir and E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl. 28 (1969), 326–329. 10.1016/0022-247X(69)90031-6Search in Google Scholar
[28]
S. A. Mohiuddine, H. M. Srivastava and A. Alotaibi,
Application of measures of noncompactness to the infinite system of second-order differential equations in
[29] M. Mursaleen, Differential equations in classical sequence spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 111 (2017), no. 2, 587–612. 10.1007/s13398-016-0301-7Search in Google Scholar
[30] M. Mursaleen and A. Alotaibi, Infinite system of differential equations in some BK spaces, Abstr. Appl. Anal. 2012 (2012), Article ID 863483. 10.1155/2012/863483Search in Google Scholar
[31] M. Mursaleen and F. Başar, Sequence Spaces: Topics in Modern Summability Theory, Math. Appl., CRC Press/Taylor & Francis Group, Boca Raton, 2020. 10.1201/9781003015116Search in Google Scholar
[32]
M. Mursaleen and S. A. Mohiuddine,
Applications of measures of noncompactness to the infinite system of differential equations in
[33]
M. Mursaleen and A. K. Noman,
On some new sequence spaces of non-absolute type related to the spaces
[34]
M. Mursaleen and S. M. H. Rizvi,
Solvability of infinite systems of second order differential equations in
[35] M. N. O. Poreli, On the neural equations of Cowan and Stein, Util. Math. 2 (1972), 305–315. Search in Google Scholar
[36] H. Roopaei and F. Başar, On the gamma spaces including the spaces of absolutely p-summable, null, convergent and bounded sequences, Numer. Funct. Anal. Optim. 43 (2022), no. 6, 723–754. 10.1080/01630563.2022.2056200Search in Google Scholar
[37] M. Stieglitz and H. Tietz, Matrixtransformationen von Folgenräumen. Eine Ergebnisübersicht, Math. Z. 154 (1977), no. 1, 1–16. 10.1007/BF01215107Search in Google Scholar
[38] B. C. Tripathy, Matrix transformation between some classes of sequences, J. Math. Anal. Appl. 206 (1997), no. 2, 448–450. 10.1006/jmaa.1997.5236Search in Google Scholar
[39] M. E. Waddill, The Tetranacci sequence and generalizations, Fibonacci Quart. 30 (1992), no. 1, 9–20. 10.1080/00150517.1992.12429379Search in Google Scholar
[40] A. Wilansky, Summability Through Functional Analysis, North-Holland Math. Stud. 85, North-Holland, Amsterdam, 1984. Search in Google Scholar
[41] T. Yaying and F. Başar, On some lambda-Pascal sequence spaces and compact operators, Rocky Mountain J. Math. 52 (2022), no. 3, 1089–1103. 10.1216/rmj.2022.52.1089Search in Google Scholar
[42] T. Yaying and F. Başar, On some Lambda-Pascal paranormed sequence spaces, Acta Sci. Math. (Szeged) (2024), 10.1007/s44146-024-00124-y. 10.1007/s44146-024-00124-ySearch in Google Scholar
[43] T. Yaying and B. Hazarika, On sequence spaces defined by the domain of a regular tribonacci matrix, Math. Slovaca 70 (2020), no. 3, 697–706. 10.1515/ms-2017-0383Search in Google Scholar
[44] M. N. Zaveri and J. K. Patel, Binet’s formula for the Tetranacci sequence, Int. J. Sci. Res. 5 (2016), no. 12, 1911–1914. Search in Google Scholar
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Convergence of matrix transform means with respect to the Walsh–Kaczmarz system
- Analysis of the embedded cell method in 2D for the numerical homogenization of metal-ceramic composite materials
- Weighted integrability of Laguerre–Bessel transforms
- Infinitely many solutions for a p(x)-triharmonic equation with Navier boundary conditions
- Bounds of some divergence measures using Green’s function and Fink’s identity via Diamond Integrals
- Invariant pseudoparallel submanifold of an SQ-Sasakian manifolds
- Some observations on ℐ-statistically pre-Cauchy sequences of complex uncertain variables defined by Orlicz functions
- Kat\v{e}tov--Blass order and measurable filters on ℕ
- ℐ-monotonic convergence of sequences of bi-complex numbers
- On the geometry of semi-slant submanifolds of a conformal Kenmotsu manifold
- Existence of multiple unbounded solutions for a three-point boundary value problems on an infinite time scales
- A simple approach for studying stability properties of an SEIRS epidemic model
- α-, β- and γ-duals of the sequence spaces formed by a regular matrix of Tetranacci numbers
- A new notion of convergence defined by weak Fibonacci lacunary statistical convergence in normed spaces
- Recurrence relations for the joint distribution of the sum and maximum of independent random variables
- Lacunary weak convergence of sequences defined by Orlicz function
- On the stability of a double porous elastic system with visco-porous damping
Articles in the same Issue
- Frontmatter
- Convergence of matrix transform means with respect to the Walsh–Kaczmarz system
- Analysis of the embedded cell method in 2D for the numerical homogenization of metal-ceramic composite materials
- Weighted integrability of Laguerre–Bessel transforms
- Infinitely many solutions for a p(x)-triharmonic equation with Navier boundary conditions
- Bounds of some divergence measures using Green’s function and Fink’s identity via Diamond Integrals
- Invariant pseudoparallel submanifold of an SQ-Sasakian manifolds
- Some observations on ℐ-statistically pre-Cauchy sequences of complex uncertain variables defined by Orlicz functions
- Kat\v{e}tov--Blass order and measurable filters on ℕ
- ℐ-monotonic convergence of sequences of bi-complex numbers
- On the geometry of semi-slant submanifolds of a conformal Kenmotsu manifold
- Existence of multiple unbounded solutions for a three-point boundary value problems on an infinite time scales
- A simple approach for studying stability properties of an SEIRS epidemic model
- α-, β- and γ-duals of the sequence spaces formed by a regular matrix of Tetranacci numbers
- A new notion of convergence defined by weak Fibonacci lacunary statistical convergence in normed spaces
- Recurrence relations for the joint distribution of the sum and maximum of independent random variables
- Lacunary weak convergence of sequences defined by Orlicz function
- On the stability of a double porous elastic system with visco-porous damping