NEW GENERALIZED DIFFERENCE SEQUENCE SPACES AND THEIR KÖTHE-TOEPLITZ DUALS

Year 2024, Volume: 10 Issue: 2, 144 - 150, 30.12.2024

Gülcan Atıcı Turan

https://doi.org/10.51477/mejs.1588355

Abstract

We will define the sequence spaces c_0 (u,∆_v^m )_p, c(u,∆_v^m )_p and l_∞ (u,∆_v^m )_p in this article. Furthermore we give some topological properties and compute their Köthe-Toeplitz duals.

Keywords

Difference sequence spaces, α-, β- and γ- dual

References

• Kızmaz, H., “On Certain Sequence Spaces”, Canad. Math. Bull., 24, 169-176, 1981.
• Et, M., Çolak, R., “On Some Generalized Difference Sequence Spaces”, Soochow J. Math., 21, 377-386, 1995.
• Et, M., Esi, A., “On Köthe-Toeplitz Duals of Generalized Difference Sequence Spaces”, Bull Malaysian Math. Sc. Soc., 23(2), 1-8, 2000.
• Bektaş, Ç. A., Et, M., Çolak, R., “Generalized Difference Sequence Spaces and Their Dual Spaces”, J. Math. Anal. Appl., 292, 423-432, 2004.
• Et, M., Başarır, M., “On Some New Generalized Difference Sequence Spaces”, Periodica Math. Hungarica, 35(3), 169-175, 1997.
• Malkowsky, E., “A Note on the Köthe-Toeplitz Duals of Generalized Sets of Bounded and Convergent Difference Sequences”, J. Anal., 4, 81-91, 1996.
• Asma, Ç., Çolak, R., “On the Köthe-Toeplitz Duals of Some Generalized Sets of Difference Sequences”, Dermonstratio Math., 4 , 797-803, 2000.
• Bektaş, Ç. A., “On Some New Generalized Sequence Spaces”, J. Math. Anal. Appl., 277, 681-688, 2003.
• Barlak D., Bektaş Ç.A., “Duals of generalized Orlicz Hilbert sequence spaces and matrix transformations”, Filomat, 31(27), 9089-9102, 2023.
• Bektaş, Ç. A., “On Some Generalized Difference Sequence Spaces and Köthe Toeplitz Duals”, IeJEMTA, 7, 61-72, 2009.
• Bektaş, Ç. A., “Absolute and Ordinary Köthe-Toeplitz Duals of Some Generalized Sets of Difference Sequences”, Hokkaido Mathematical Journal, 33(1), 207-214, 2004.