SOME GEOMETRIC PROPERTIES OF THE DOMAIN OF THE TRIANGLE e A IN THE SEQUENCE SPACE `(p)

Year 2014, Volume: 63 Issue: 2, 163 - 176, 01.08.2014

Esra Sümeyra Yılmaz Feyzi Başar

https://doi.org/10.1501/Commua1_0000000721

Cited By: 1

https://izlik.org/JA36WP94LN

Keywords

Paranormed sequence spaces , triangle matrix , alpha- , beta- andgamma-duals , matrix transformations and rotundity of a sequence space

References

• [1]
• [2] I.J. Maddox, Spaces of strongly summable sequences, Quart. J. Math. Oxford (2) 18 (1967), 345ñ355.
• [3] S. Simons, The sequence spaces `(pv) and m(pv), Proc. London Math. Soc. (3), 15 (1965), 422ñ436.
• [4] H. Nakano, Modulared sequence spaces, Proc. Japan Acad. 27 (2) (1951), 508ñ512.
• [5] A.M. Jarrah, E. Malkowsky, BK spaces, bases and linear operators, Rendiconti Circ. Mat. Palermo II 52 (1990), 177ñ191.
• [6] B. Altay, F. Ba¸sar, On the paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bull. Math. 26 (5) (2002), 701ñ715.
• [7] S. Chen, Geometry of Orlicz Spaces, Dissertationes Math. 356 (1996), 1ñ224.
• [8] J. Diestel, Geometry of Banach Spaces - Selected Topics, Springer - Verlag, 1984.
• [9] L. Maligranda, Orlicz Spaces and Interpolation, Inst. Math. Polish Academy of Sciences, Poznan,1985.
• [10] C. Ayd¨n, F. Ba¸sar, Some generalizations of the sequence space a r p , Iran. J. Sci. Technol. Trans. A, Sci. 30 (2006), No. A2, 175ñ190.
• [11] C. Ayd¨n, F. Ba¸sar, Some topological and geometric properties of the domain of the generalized di§ erence matrix B(r; s) in the sequence space `(p), Thai J. Math. 12 (1) (2014), 113ñ132.
• [12] F. Ba¸sar, B. Altay, M. Mursaleen, Some generalizations of the space bvp of p-bounded variation sequences, Nonlinear Anal. 68 (2) (2008), 273ñ287.
• [13] H. Nergiz, F. Ba¸sar, Some topological and geometric properties of the domain of the double sequential band matrix B(r; e se) in the sequence space `(p), AIP Conference Proceedings 1470 (2012), 163ñ168, doi: 10.1063/1.4747665.
• [14] H. Nergiz, F. Ba¸sar, Some geometric properties of the domain of the double sequential band matrix B(r; e se) in the sequence space `(p), Abstr. Appl. Anal. 2013, Article ID 421031, 7 pages, 2013. doi: 10.1155/2013/421031.
• [15] E. UÁar, F. Ba¸sar, Some geometric properties of the domain of the double band matrix deÖned by Fibonacci numbers in the sequence space `(p), AIP Conference Proceedings 1611 (2014), 316ñ324, doi: 10.1063/1.4893854.
• [16] M. Ye¸silkayagil, F. Ba¸sar, On the paranormed Nˆrlund sequence space of non-absolute type, Abstr. Appl. Anal. 2014, Article ID 858704, 9 pages, 2014. doi:10.1155/2014/858704.
• [17] E.E. Kara, Some topological and geometrical properties of new Banach sequence spaces, J. Inequal. Appl. 2013, 15 pages, 2013. doi:10.1186/1029-242X-2013-38.
• [18] M. Ba¸sar¨r, F. Ba¸sar, E.E. Kara, On the spaces of Fibonacci di§ erence null and convergent sequences, arXiv:1309.0150v1 [math.FA], (2013).