SOME NOTES ON THE SEQUENCE SPACES LΛP(GM) AND LΛ∞(GM)S

Year 2017, Volume: 30 Issue: 1, 381 - 393, 14.03.2017

Mustafa Cemil Bişgin

https://izlik.org/JA42CS28LS

Abstract

In this work, we introduce the sequence spaces lλp (Gm) and lλ∞(Gm) derived by the domain of the composition of m−th order generalized difference matrix and lambda matrix. Moreover, we determine some topological properties and examine inclusion relations related to these spaces. Furthermore, we give Schauder basis for the space lλp (Gm ). Finally, we determine α−, β− and γ−duals of the spaces lλp(Gm) and lλ∞ (Gm ). 

Keywords

Sequence Space , Matrix Transformation; Matrix Domain; Schauder Basis; α− , β− and γ−Duals; Topological Property

References

• Basar, F.; Karaisa, A. Some new generalized difference spaces of non absolute type derived from the spaces lp and l∞. The Scientific World J. 2013, (2013).
• Basarır, M.; Kayıkc ̧ı, M. On generalized Bm-Riesz difference sequence space and β-property. J. Inequal. Appl., 2013,(2009).
• Choudhary, B.; Nanda, Sudarsan. Functional Analysis with Applications, John Wiley & sons Inc., New York, 1989.
• Et, M. On Some Difference Sequence Spaces. Turkish J. Math. 17 (1993) 18-24.
• Et, M.; Colak, R. On some generalized difference sequence spaces. Soochow J.
• Math. 21 (4) (1995) 377-386.
• Kızmaz, H. On certain sequence spaces. Canad. Math. Bull. 24(1981), no. 2, 169-176.
• Maddox, I. J. Elements of Functional Analysis. Second edition. Cambridge Univer-
• sity Press, Cambridge, (1988).
• Malkowsky, E. Recent results in the theory of matrix transformations in sequence
• spaces. Mat. Vesnik 49(1997), 187-196.
• Mursaleen, M.; Noman, Abdullah K. On some new sequence spaces of non-
• absolute type related to the spaces lp and l∞ I. Filomat 25 (2011), no. 2, 33-51.
• Mursaleen, M.; Noman, Abdullah K. On some new sequence spaces of non- absolute type related to the spaces lp and l∞ II. Math. Commun. 16 (2011), no. 2,
• –398.
• Ng, P. -N. ; Lee, P. -Y. Cesa`ro sequence spaces of non–absolute type, Comment.
• Math. Prace Mat. 20 (1977/78), no. 2, 429–433.
• Sonmez, A. Some new sequence spaces derived by the domain of the triple band
• matrix. Comput. Math. Appl. 62 (2011), no. 2, 641–650.
• Stieglitz, Michael; Tietz, Hubert Matrixtransformationen von Folgenrumen.
• Eine Ergebnisbersicht. (German)Math. Z. 154 (1977), no. 1, 1–16.
• Wang, C. -S. On No ̈rlund sequence spaces. Tamkang J. Math. 9(1978), 269–274.
• Wilansky, Albert Summability through functional analysis.North-Holland Math-
• ematics Studies. 85. Notas de Matemtica [Mathematical Notes], 91. North-Holland Publishing Co., Amsterdam, (1984).