The Application Domain of Infinite Matrices with Algorithms

Year 2018, Volume: 1 Issue: 1, 1 - 9, 11.03.2018

Murat Kirişçi

https://doi.org/10.32323/ujma.376585

Cited By: 6

Abstract

The purpose of this paper is twofold. First, we define the new spaces and investigate some topological and structural properties. Also, we compute dual spaces of new spaces which are help us in the characterization of matrix mappings. Second, we give some examples related to new spaces. A flow chart of the stages of the newly constructed sequence spaces and the algorithms of the workings at each step are given.  

Keywords

Schauder basis, AK-property, Algorithm, Flowchart, Matrix domain, Dual space, Monotone norm

References

• [1] B. Altay and F. Bas¸ar, Certain topological properties and duals of the domain of a triangle matrix in a sequence spaces, J. Math. Analysis and Appl., 336 (2007), 632–645.
• [2] B. Altay, F. Bas¸ar, On some Euler sequence spaces of non-absolute type, Ukrainian Math. J. 57(1)(2005), 1–17.
• [3] F. Başar and B. Altay On the space of sequences of p-bounded variation and related matrix mappings, Ukranian Math. J., 55(1) (2003), 136–147.
• [4] B. Altay, F. Başar, M. Mursaleen, On the Euler sequence spaces which include the spaces $l_p$ and $l_\infty$, I Inform. Sci. 176(10)(2006), 1450–1462.
• [5] M. Kirisci, Integrated and differentiated sequence spaces, 2015(1), (2015), Article ID: jnna-00266, 2–16, doi: 10.5899/2015/jnaa-00266.
• [6] M. Kirişçi, On the Taylor sequence spaces of nonabsolute type which include the spaces c0 and c,J. Math. Anal., 6(2), 22–35, (2015). [7] E. Malkowsky, Recent results in the theory of matrix transformations in sequence spaces, Mat. Ves. 49, 187–196, (1997).
• [8] P.-N., Ng, P. -Y., Lee, : Ces`aro sequence spaces of non-absolute type, Comment. Math. Prace Mat. 20(2), 429–433, (1978).
• [9] A. Wilansky, Summability through Functional Analysis, North- Holland (1984).