Paranormed spaces of absolute tribonacci summable series and some matrix transformations
DOI:
https://doi.org/10.56405/dngcrj.2024.09.01.02Keywords:
Absolute Summability, Matrix Transformations, Maddox spaceAbstract
In a more recent paper, the absolute series space I T_\Phi I_q which is defined as the domain of the matrix corresponding to the absolute Tribonacci summability in the well-known space l_q has taken place in the literature (Gökçe, in press). The present study is mainly aimed to establish the absolute series space I T_\Phi I(\delta) which includes I T_\Phi I_q as the set of all series summable by the absolute Tribonacci method in l(\delta), and to investigate its some topological and algebraic properties. Moreover, certain characterizations of matrix operators on this space is obtained.
Downloads
References
Dağlı, M.C., & Yaying, T. (2023). Some new paranormed sequence spaces derived by regular Tribonacci matrix. The Journal of Analysis, 31(1), 109-127.
Gökçe, F., (2021). Compact and Matrix Operators on the Space |N ̅_P^θ |_k. Fundamental Journal of Mathematics and Applications 4 (2), 124-133.
Gökçe, F. (2022). Compact matrix operators on Banach space of absolutely k-summable series. Turkish Journal of Mathematics, 46(3), 1004-1019.
Gökçe, F. (2025). On absolute Tribonacci series spaces and some matrix operators. Mathematical Sciences and Applications E-Notes, 13(1), 1-11.
Gökçe, F., & Sarıgöl, M.A. (2020). Some matrix and compact operators of the absolute Fibonacci series spaces. Kragujevac Journal of Mathematics, 44 (2), 273–286,
Gökçe, F., & Sarıgöl, M.A. (2020a). On absolute Euler spaces and related matrix operators. Proceedings of the National Academy of Sciences, India. Section A. Physical Sciences, 90(5), 769-775
Gökçe, F., & Sarıgöl, M.A. (2020b). Series spaces derived from absolute Fibonacci summability and matrix transformations. Bollettino dell'Unione Matematica Italiana, 13, 29-38
Gökçe, F., & Sarıgöl, M.A. (2019). Generalization of the absolute Cesaro space and some matrix transformations. Numerical Functional Analysis and Optimization , 40, 1039-1052
Gökçe, F., & Sarıgöl, M.A. (2019a). Extension of Maddox’s space l(μ) with Nörlund means. Asian-European Journal of Mathematics, 12(6), 2040005.
Gökçe, F., & Sarıgöl, M.A. (2018). Generalization of the space l(p) derived by absolute Euler summability and matrix operators. Journal of Inequalities and Applications, 2018, 133.
Gökçe, F., & Sarıgöl, M.A. (2018a). A new series space |〖 N ̅〗_p^θ |(μ) and matrix transformations with applications. Kuwait Journal of Science, 45 (4), 1-8.
Grosse-Erdmann, K.G. (1993). Matrix transformations between the sequence spaces of Maddox. Journal of Mathematical Analysis and Applications, 180, 223-238
Maddox, I. J. (1967). Spaces of strongly summable sequences. The Quarterly Journal of Mathematics, 18, 345-355.
Maddox, I. J. (1968). Paranormed sequence spaces generated by infinite matrices. Mathematical Proceedings of the Cambridge Philosophical Society, 64, 335-340.
Maddox, I. J. (1969). Some properties of paranormed sequence Spaces. Journal of the London Mathematical Society. Second Series, 316-322.
Malkowsky, E., Rakocevic, V. (2000). An introduction into the theory of sequence space and measures of noncompactness. Zbornik. Radova (Beogr), 9 (17), 143-234.
Malkowsky, E., Rakocevic V. (2007). On matrix domains of triangles. Applied Mathematics Computations. 189 (2), 1146-1163.
Sarıgöl, M.A. (2010). On the local properties of factored Fourier series. Applied Mathematics Computations 216 (11), 3386-3390
Sarıgöl, M.A. (2013). An inequality for matrix operators and its applications. Journal of Classical Analysis, 2, 145-150.
Wilansky, A., (1984). Summability through Functional Analysis. Mathematical Studies 85, North–Holland, Amsterdam.
Yaying, T., & Hazarika, B. (2020). On sequence spaces defined by the domain of a regular Tribonacci matrix. Mathematica Slovaca, 70 (3), 697-706.
Yaying, T., & Kara, M.I. (2021). On sequence spaces defined by the domain of tribonacci matrix in c_0 and c. Korean Journal of Mathematics, 29 (1), 25-40.
Downloads
Published
How to Cite
Issue
Section
License
Dera Natung Government College Research Journal retains the copyright of the article and its contents. The authors are expected to obtain permission from the journal if they choose to reuse the article under Creative Commons Attribution 4.0 International License (CC BY 4.0). Upon having received the journal’s permission, this open license would allow the authors for reuse or adaptation as long as their original article is properly and adequately cited.
