Domain of the matrix A_\lambda in the space of p-bounded variation sequences
Abstract
In this paper, we defined the sequence space $\mathcal{A}_\lambda(bv_p)$ of $p$-bounded variation using the triangle matrix $\mathcal{A}_\lambda$ of non-absolute type. We analyzed the topological properties and defined the Schauder basis of the sequence space $\mathcal{A}_\lambda(bv_p)$. Also, the Kothe duals of $\mathcal{A}_\lambda(bv_p)$ have been computed. Finally, we characterize certain classes of matrix transformations concerning this sequence space.
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References
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2. B. Altay and F. Ba\c{s}ar, Some Euler sequences spaces of non-absolute type, Ukrainaina Math. J. {\bf1} (2005), 1-17.
\bibitem{B. Altay2} B. Altay and F. Ba\c{s}ar, M. Mursaleen, On the Euler sequence spaces which include the spaces $\ell_p$ and $\ell_\infty$ Inform. Sci. {\bf176} (10) (2006), 1450-1462.
3. B. Altay, F. Ba\c{s}ar, E. Malkowsky, Matrix transformations on some sequence spaces related to strong Cesaro summability and boundedness, Appl. Math. Comput. {\bf211} (2009), 255–264.
4. C. Ayd{\i}n, F. Ba\c{s}ar, On the new sequence spaces which include the spaces $c_0$ and $c$, Hokkaido Math. J. {\bf33} (2) (2004), 383–398.
5. C. Ayd{\i}n, F. Ba\c{s}ar, Some new difference sequence spaces, J. of Appl. Math. and Comput. {\bf3} (2002), 27-40.
6. F. Ba\c{s}ar, Summability Theory and Its Applications, $2^{nd}$ ed., CRC Press/Taylor, Francis Group, Boca Raton. London. New York, 2022.
7. F. Ba\c{s}ar, B. Altay, On the spaces of $p$-bounded variation and related matrix mappings, Ukrainian Math. J. {\bf55} (2003), 136-147.
8. F. Ba\c{s}ar, B. Altay, M. Mursaleen, Some generalizations of the space $bv_p$ of $p$-bounded variation sequences, Nonlinear Anal. {\bf68} (2008), 273-287.
9. F. Ba\c{s}ar, M. Kiri\c{s}\c{c}i, Almost convergence and generalized difference matrix, Comput. Math. Appl. {\bf61} (3) (2011), 602–611.
10. F. Ba\c{s}ar, E. Malkowsky, B. Altay, Matrix transformations on the matrix domains of triangles in the spaces of strongly $C_1$–summable and bounded sequences, Publ. Math. Debrecen {\bf73} (1-2) (2008), 193–213.
11. J. Boos, Classical and modern methods in summability, Oxford University Press, New York, 2000.
12. N. L. Braha, F. Ba\c{s}ar, On the domain of the triangle $A(\lambda)$ on the spaces of null, convergent and bounded sequences, Abstr. Appl. Anal. {\bf1} (9) (2013).
13. M. Kiri\c{s}\c{c}i, F. Ba\c{s}ar, Some new sequence spaces derived by the domain of generalized difference matrix, Comput. Math. Appl. {\bf60} (5) (2010), 1299–1309.
14. H. K{\i}zmaz, On Certain Sequence Spaces. Canad. Math. Bull. {\bf24} (2) (1981), 169-176.
15. I.J. Maddox, Elements of Functional Analysis, 2nd ed., The University Press, Cambridge, 1988.
16. E. Malkowsky, Recent results in the theory of matrix transformations in sequence spaces, Mat. Vesnik {\bf49} (209) (1997), 187-196
17. M. Mursaleen, F. Ba\c{s}ar, Sequence Spaces: Topics in Modern Summability Theory, CRC Press, Taylor and Francis Group, Series: Mathematics and Its Applications, Boca Raton. London. New York, 2020.
18. M. Mursaleen, F. Ba\c{s}ar, B. Altay, On the Euler sequence spaces which include the spaces $\ell_p$ and $\ell_\infty$-II, Nonlinear Anal., {\bf65} (3) (2006), 707-717.
19. P. N. Ng and P. Y. Lee, Ces\`aro sequence spaces of non-absolute type, Comment. Math. {\bf20} (2) (1978), 429–433.
20. N.A. Sheikh, A.H. Ganie, A new paranormed sequence space and some matrix transformations, Acta Math. Acad. Paedagog. Nyhazi. (N.S.) {\bf28} (2012), 47-58.
21. M. Stieglitz and H. Tietz, Matrixtrans formationen von folgenraumen. Eine ergebnisubersicht, Math. Z. {\bf154} (1) (1977), 1-16.
22. C.S. Wang, On N\"{o}rlund sequence spaces, Tamkang J. Math. {\bf9} (1978), 269-274.
23. A. Wilansky, Summability through functional analysis, 1st Edition, North-Holland Mathematics Studies, 2000.
24. M. Ye\c{s}ilkayagil, F. Ba\c{s}ar, Spaces of $A_\lambda$-almost null and $A_\lambda$-almost convergent sequences, J. Egyptian Math. Soc. {\bf23} (1) (2014), 119-126.
Published
2026-04-17
Section
Special Issue: Advances in Nonlinear Analysis and Applications
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